Citations with the tag: RICCATI equation

Results 51 - 100

  • Sufficient Conditions for Stabilizability of Linear Periodic Differential Equations.
    Phat, Vu Ngoc // Southeast Asian Bulletin of Mathematics; 2006, Vol. 30 Issue 2, p331 

    This paper studies a stabilizability problem for linear time-varying periodic differential equations. Based on the Floquet theory and discretization method, we give new sufficient conditions for stabilizability in terms of controllability rank condition of linear time-invariant discretized...

  • Uniformly exponentially stable approximations for a class of second order evolution equations.
    Karim Ramdani; Tak?o Takahashi; Marius Tucsnak // ESAIM: Control, Optimisation & Calculus of Variations; Jul2007, Vol. 13 Issue 3, p503 

    We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite...

  • Traveling Wave Solutions and Soliton Solutions for A Generalized Burgers Equation with Variable Coefficients Using Symbolic Computation.
    El-Boree, Mohammed Khalfallah // Journal of Modern Methods in Numerical Mathematics; 2011, Vol. 2 Issue 1/2, p45 

    We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the generalized Burgers equation with variable coefficients. Many exact traveling wave solutions are successfully obtained, which contain soliton, soliton-like solutions,...

  • Design of discrete H2-optimal reduced-order controllers.
    Lutsenko, I.; Sadomtsev, Yu. // Automation & Remote Control; Oct2009, Vol. 70 Issue 10, p1698 

    Consideration was given to the design of discrete dynamic reduced-order controllers minimizing the H2-norm of the transfer matrix of a closed-loop system. The problem of reducing the controller order is related to the solution of the singular problem of filtration (no measurement noise) and...

  • OSCILLATION CRITERIA FOR THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES.
    TONGXING LI; ZHENLAI HAN; CHENGHUI ZHANG; YING SUN // Bulletin of Mathematical Analysis & Applications; Mar2011, Vol. 3 Issue 1, p52 

    By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. on a time scale ? unbounded above, here ? > 0 is a quotient...

  • Criteria for exponential stability of linear differential equations with positive evolution on ordered Banach spaces.
    DRAGAN, VASILE; MOROZAN, TOADER // IMA Journal of Mathematical Control & Information; Sep2010, Vol. 27 Issue 3, p267 

    In this paper, the problem of exponential stability of the zero state equilibrium of a linear differential equation defined by an operator-valued function with positive evolution on an infinite-dimensional ordered Banach space is investigated. The class of linear differential equations...

  • Linear quadratic regulator for time-varying hyperbolic distributed parameter systems.
    AKSIKAS, ILYASSE; FORBES, J. FRASER // IMA Journal of Mathematical Control & Information; Sep2010, Vol. 27 Issue 3, p387 

    This paper addresses the linear quadratic (LQ) problem for a class of time-varying hyperbolic partial differential equation (PDEs) systems. The control method is based on two main ingredients: infinite-dimensional state space description and the well-known Riccati equation approach. First, the...

  • Improving the Accuracy of the Solutions of Riccati Equations.
    Vahidi, A. R.; Didgar, M. // International Journal of Industrial Mathematics; 2012, Vol. 4 Issue 1, p11 

    In this paper, we present an improved method for solving Riccati equations. This modification is based on the previous scheme to obtain the approximate solution of Riccati equations [B.Q. Tang and X.F. Li, A new method for determining the solution of Riccati differential equations, Appl. Math....

  • Classical Solutions of Nonautonomous Riccati Equations Arising in Parabolic Boundary Control Problems, II.
    Acquistapace, P.; Terreni, B. // Applied Mathematics & Optimization; 2000, Vol. 41 Issue 2, p199 

    Abstract. An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. We give the proof of some result stated in [AT5], and in...

  • On the Stabilization of Nonlinear Continuous-Time Systems in Hilbert Spaces.
    Phat, Vu N.; Linh, Nguyen M. // Southeast Asian Bulletin of Mathematics; 2003, Vol. 27 Issue 1, p135 

    This paper deals with stabilization problem of a class of infinite-dimensional nonlinear continuous-time systems. We present some useful relations between infinite-dimensional controllability and Riccati operator equations in Hilbert spaces and then apply to the complete stabilization problem....

  • A method of constructing Lyapunov functions of continuous TSK fuzzy model.
    ZHIGANG YU; QI FEI // IMA Journal of Mathematical Control & Information; Sep2005, Vol. 22 Issue 3, p251 

    Stability of system with continuous TSK fuzzy model is analysed on the basis of Tanaka's theorem. An approach to construct Lyapunov's functions of a class of systems by solving Riccati inequalities or Riccati equations is presented.

  • The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations.
    Jianping Zhao; Bo Tang; Kumar, Sunil; Yanren Hou // Mathematical Problems in Engineering; 2012, Vol. 2012, Special section p1 

    An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansatz and Backlund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time...

  • The Three-Step Master Equation: Class of Parametric Stationary Solutions.
    Rosu, Haret C.; Reyes, Marco A.; Valencia, F. // International Journal of Theoretical Physics; Sep2005, Vol. 44 Issue 9, p1565 

    We examine the three-step master equation from the standpoint of the general solution of the associated discrete Riccati equation. We report by this means stationary master solutions depending on a free constant parameter, denoted by D, that should be negative in order to assure the positivity...

  • A Riccati equation in radiative stellar collapse.
    Rajah, S. S.; Maharaj, S. D. // Journal of Mathematical Physics; Jan2008, Vol. 49 Issue 1, p012501 

    We model the behavior of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behavior is a Riccati equation. We show that the Riccati equation admits two classes of new...

  • Evaluation and Comparison of the Performance of Two Techniques on Two Cart-Inverted Pendulum System.
    Baigzadeh, B.; Nazarzehi, V.; Khaloozadeh, H. // International Review of Automatic Control; Jul2011, Vol. 4 Issue 4, p503 

    The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel...

  • AN OPTIMAL CONSENSUS TRACKING CONTROL ALGORITHM FOR AUTONOMOUS UNDERWATER VEHICLES WITH DISTURBANCES.
    Jian Yuan; Wen-Xia Zhang; Zhou-Hai Zhou // International Journal of Instrumentation & Control Systems; Apr2012, Vol. 2 Issue 2, p45 

    The optimal disturbance rejection control problem is considered for consensus tracking systems affected by external persistent disturbances and noise. Optimal estimated values of system states are obtained by recursive filtering for the multiple autonomous underwater vehicles modeled to...

  • On Lie systems and Kummer-Schwarz equations.
    de Lucas, J.; Sardón, C. // Journal of Mathematical Physics; Mar2013, Vol. 54 Issue 3, p033505 

    A Lie system is a system of first-order differential equations admitting a superposition rule, i.e., a map that expresses its general solution in terms of a generic family of particular solutions and certain constants. In this work, we use the geometric theory of Lie systems to prove that the...

  • Stochastic Linear Quadratic Optimal Control Problems with Random Coefficients.
    Chen, Shuping; Yong, Jiongmin // Chinese Annals of Mathematics; Jul2000, Vol. 21 Issue 3, p323 

    This paper studies a stochastic linear quadratic optimal control problem (LQ problem, for short), for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. The authors introduce the stochastic Riccati...

  • Comparative index for solutions of symplectic difference systems.
    Eliseeva, Yu. // Differential Equations; Mar2009, Vol. 45 Issue 3, p445 

    We introduce the comparative index of two conjoined bases of a symplectic difference system, which generalizes difference analogs of canonical systems of differential equations. We consider the main properties of the comparative index and its relation to the number of focal points of a conjoined...

  • A GEOMETRIC APPROACH TO INTEGRABILITY CONDITIONS FOR RICCATI EQUATIONS.
    Cariñena, José F.; De Lucas, Javier; Ramos, Arturo // Electronic Journal of Differential Equations; 2007, Vol. 2007, p1 

    Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.

  • OSCILLATION OF SECOND-ORDER NONLINEAR IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES.
    Mugen Huang; Weizhen Feng // Electronic Journal of Differential Equations; 2007, Vol. 2007, p1 

    In this article, we study the oscillation of second-order nonlinear impulsive dynamic equations on time scales. Using Riccati transformation techniques, we obtain sufficient conditions for oscillation of all solutions. An example is given to show that the impulses play a dominant part in...

  • The WKB method and differential consequences of the Riccati equation.
    Chuprikov, N. L. // Mathematical Notes; Jun2011, Vol. 89 Issue 5/6, p885 

    generalized WKB method based on the use of the differential consequences of the Riccati equation is presented. The method combines the simplicity of the traditional WKB method and the universality of the Maslov method: in the case of a smooth potential with classical turning points in a bounded...

  • Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach.
    Dimakis, A.; Müller-Hoissen, F. // Theoretical & Mathematical Physics; Jul2007, Vol. 152 Issue 1, p933 

    Functional representations of (matrix) Burgers and potential Kadomtsev-Petviashvili (pKP) hierarchies (and others), as well as some corresponding Bäcklund transformations, can be obtained surprisingly simply from a “discrete” functional zero-curvature equation. We use these...

  • Finding the strongly rank-minimizing solution to the linear matrix inequality.
    Chaikovskii, M. M. // Automation & Remote Control; Sep2007, Vol. 68 Issue 9, p1559 

    Consideration is given to an nonstrict linear matrix inequality and associated Riccati equation that occurs on solving problems of analysis and synthesis of linear stationary discrete time systems. The strongly rank-minimizing solution to the considered linear matrix inequality also satisfies...

  • Stabilization of linear autonomous systems of differential equations with distributed delay.
    Dolgii, Yu. F. // Automation & Remote Control; Oct2007, Vol. 68 Issue 10, p1813 

    Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that...

  • On general solutions of particular classes of linear nonhomogeneous second-order equations with variable coefficients.
    Kharatishvili, G. // Journal of Mathematical Sciences; Jan2008, Vol. 148 Issue 3, p293 

    The author states and proves main theorems implying theorems on general solutions of particular classes of linear nonhomogeneous second-order equations with variable coefficients, in particular, those for certain classes of generalized and canonical equations of Heun, Lamé, Gauss, and Legendre.

  • Constructive methods for obtaining the solution of the periodic boundary value problem for a system of matrix differential equations of Riccati type.
    Laptinskii, V.; Rogolev, D. // Differential Equations; Oct2011, Vol. 47 Issue 10, p1426 

    In the nonsingular case, we obtain sufficient coefficient conditions for the unique solvability of the periodic boundary value problem for a system of matrix differential equations of Riccati type. We develop efficient algorithms for constructing the solution.

  • A computational method for interval mixed variable energy matrices in precise integration.
    Suo-wen Gao; Zhi-gang wu; Ben-li Wang; Xing-rui Ma // Applied Mathematics & Mechanics; May2001, Vol. 22 Issue 5, p557 

    To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the...

  • A Computational Method for Interval Mixed Variable Energy Matrices in Precise Integration.
    Suo-wen Gao; Zhi-gang Wu; Ben-li Wang; Xing-rui Ma // Applied Mathematics & Mechanics; May2001, Vol. 22 Issue 5, p557 

    To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the...

  • ∞-symmetries and nonlocal symmetries of exponential type.
    MURIEL, C.; ROMERO, J. L. // IMA Journal of Applied Mathematics; Apr2007, Vol. 72 Issue 2, p191 

    Nonlocal symmetries generated by type I hidden symmetries are identified as specific ∞-symmetries of an nth-order ordinary differential equation. The general method of reduction associated to these ∞-symmetries allows us to give explicit transformations to reduce the order...

  • New characterization of controllability via stabilizability and Riccati equation for LTV systems.
    PHAT, V. N.; HA, Q. P. // IMA Journal of Mathematical Control & Information; Dec2008, Vol. 25 Issue 4, p419 

    This paper presents a new characterization of controllability via stabilizability and Riccati equation for linear time-varying systems. An equivalence is given between the global null controllability, complete stabilizability and the existence of the solution of some appropriate Riccati...

  • Möbius Transformations and Periodic Solutions of Complex Riccati Equations.
    Campos, Juan // Bulletin of the London Mathematical Society; 1997, Vol. 29 Issue 2, p205 

    In this paper we are going to study the solutions of a complex T-periodic Riccati equation z′=z2+p(t), and we are going to determine all the possible dynamics of this type of equation. Also, we can say that generically there are two different T-periodic solutions. 1991 Mathematics Subject...

  • VIM for Solving the Pollution Problem of a System of Lakes.
    Biazar, J.; Shahbala, M.; Ebrahimi, H. // Journal of Control Science & Engineering; 2010, Special section p1 

    Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. In this paper the pollution problem of three lakes with interconnecting...

  • On the properties of the identically singular Lagrange problem.
    Chistyakov, V.; Peshich, M. // Automation & Remote Control; Jan2009, Vol. 70 Issue 1, p74 

    We consider the identically singular Lagrange problem of the calculus of variations. It is investigated how the conjugate points and the Jacobi equation index are related to the solvability conditions of the appropriate matrix Riccati equation and the reducibility of the functional to a perfect...

  • On Linearization by Generalized Sundman Transformations of a Class of Liénard Type Equations and Its Generalization.
    Johnpillai, A. G.; Mahomed, F. M. // Applied Mathematics & Information Sciences; 2013, Vol. 7 Issue 6, p2355 

    We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map...

  • The Taylor Matrix Method for Approximate Solution of Lane-Emden Equation with index-n.
    Guler, Coskun; Emiroglu, Ibrahim; Tasci, Fatih; Sivri, Mustafa // Applied Mathematics & Information Sciences; Jul2013, Vol. 7 Issue 4, p1341 

    Many problems in mathematical physics can be formulated as an equation of Lane-Emden type. There are many methods for the solution of this equation. One of these methods is the Taylor matrix method. The only types of nonlinear equations that this method has been applied so far are the Riccati...

  • HIV-INFECTION MODEL STABILIZATION.
    V., Kim A.; M., Kormyshev V.; A., Safronov M. // In the World of Scientific Discoveries / V Mire Nauchnykh Otkryt; 2013, Issue 46, p218 

    In the paper considers a problem of stabilizing a mathematical model of HIV dynamics is considered. The model is described by a system of functional differential equations. A stabilizing control is constructed basing on the method of explicit solutions of Generalized Riccati Equations of the...

  • Oscillation results for even order functional dynamic equations on time scales.
    Tunç, Ercan // Electronic Journal of Qualitative Theory of Differential Equatio; 2014, Issue 4-30, p1 

    By employing a generalized Riccati type transformation and the Taylor monomials, some new oscillation criteria for the even order functional dynamic equation (r(t)|xΔn-1 (t)|α-1 xΔn-1 (t)) Δ + F(t,x(t),x(τ(t)),xΔ (t),xΔ (τ(t))) = 0,t∈ [t0, ∞)T, are...

  • Generalized Riccati equations for self-dual Yang–Mills fields.
    Chau, L.-L.; Yen, H. C. // Journal of Mathematical Physics; May87, Vol. 28 Issue 5, p1167 

    It is shown that although no Riccati equations in the strict sense are likely to exist for the self-dual Yang–Mills fields, certain ‘‘generalized Riccati equations’’ derivable from the Bäcklund transformation do exist, and are capable of reproducing the linear...

  • Precise Solution of the Algebraic Riccati Equation for One-Input Relaxation Systems.
    Borukhov, V. T.; Zelenyak, D. M. // Automation & Remote Control; Apr2003, Vol. 64 Issue 4, p531 

    Consideration was given to a special class of the algebraic Riccati equations arising in the theory of one-input relaxation systems. The precise solution obtained was used for rational parametrization of the dissipative manifold and the boundary of the set of solutions of the dissipative inequality.

  • OSCILLATION OF SOLUTIONS TO IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES.
    QIAOLUAN LI; FANG GUO // Electronic Journal of Differential Equations; 2009, Vol. 2009, Special section p1 

    In this article, we study the oscillation of second order impulsive dynamic equations on time scales. The effect of the moments of impulse are fixed. Using Riccati transformation techniques, we obtain some conditions for the oscillation of all solutions.

  • New Trace Bounds for the Product of Two Matrices and Their Applications in the Algebraic Riccati Equation.
    Jianzhou Liu; Juan Zhang // Journal of Inequalities & Applications; 2009, Vol. 2009, Special section p1 

    By using singular value decomposition and majorization inequalities, we propose new inequalities for the trace of the product of two arbitrary real square matrices. These bounds improve and extend the recent results. Further, we give their application in the algebraic Riccati equation. Finally,...

  • Synthesis of linear quadratic control laws on basis of linear matrix inequalities.
    Balandin, D.; Kogan, M. // Automation & Remote Control; Mar2007, Vol. 68 Issue 3, p371 

    Classic problems of control law construction for a linear dynamic object that is optimal by the quadratic criterion in the determinate and stochastic cases are reduced, as is known, to solving nonlinear matrix Riccati equations. It is shown that the notion of H 2-norm of a system transfer matrix...

  • On Algebraic Approach in Quadratic Systems.
    Mencinger, Matej // International Journal of Mathematics & Mathematical Sciences; 2011, p1 

    When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and...

  • OSCILLATION FOR FORCED SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES.
    Mugen Huang; Weizhen Feng // Electronic Journal of Differential Equations; 2006, Vol. 2006, Special section p1 

    By means of Riccati transformation techniques, we present oscillation criteria for forced second-order nonlinear dynamic equations on time scales. These results are based on the information on a sequence of subintervals of [a, ∞) only, rather than on the whole half-line.

  • WAVE REFLECTION AND TRANSMISSION FROM ANISOTROPIC LAYERS THROUGH RICCATI EQUATIONS.
    CAVIGLIA, GIACOMO; MORRO, ANGELO // Quarterly Journal of Mechanics & Applied Mathematics; Feb2002, Vol. 55 Issue 1, p93 

    Reflection and transmission matrices, associated with obliquely-incident plane harmonic waves, are investigated for a planarly-stratified inhomogeneous layer. The material in the layer and in the half-spaces is a dissipative anisotropic solid. Upon establishing a Cauchy problem for the local...

  • Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales.
    Şenel, M. Tamer // Abstract & Applied Analysis; 2012, p1 

    The oscillation of solutions of the second-order nonlinear dynamic equation (r(t)(x▵(t))Γ )▵ + p(t)(x▵(t))Γ + f(t, x(g(t))) = 0, with damping on an arbitrary time scale T, is investigated. The generalized Riccati transformation is applied for the study of the...

  • A computational approach to continuum damping of Alfvén waves in two and three-dimensional geometry.
    Könies, Axel; Kleiber, Ralf // Physics of Plasmas; Dec2012, Vol. 19 Issue 12, p122111 

    While the usual way of calculating continuum damping of global Alfvén modes is the introduction of a small artificial resistivity, we present a computational approach to the problem based on a suitable path of integration in the complex plane. This approach is implemented by the Riccati...

  • Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities.
    Jing Shao; Fanwei Meng; Xinqin Pang // Discrete Dynamics in Nature & Society; 2012, Special section p1 

    Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature.

  • DEFLATING IRREDUCIBLE SINGULAR M-MATRIX ALGEBRAIC RICCATI EQUATIONS.
    WEI-GUO WANG; WANG, WEI-CHAO; LI, REN-CANG // Numerical Algebra, Control & Optimization; Sep2013, Vol. 3 Issue 3, p491 

    A deflation technique is presented for an irreducible singular M- matrix Algebraic Riccati Equation (MARE). The technique improves the rate of convergence of a doubling algorithm, especially for an MARE in the critical case for which without deflation the doubling algorithm converges linearly...

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