## Citations with the tag: RICCATI equation

### Results 51 - 100

- Oscillation of Second Order Neutral Differential Equations.

Yong Xia; Zhiting Xu // Southeast Asian Bulletin of Mathematics; 2006, Vol. 30 Issue 1, p157Using the generalized Riccati technique and the averaging technique, new oscillation criteria for second order neutral differential equation [a(t)(x(t) - p(t)x(t - T))']' + q(t)f[x(t), x(t - s)]g[x'(t)] = 0 are obtained. These results extend and improve the oscillation criteria given by Ruan, Li...

- Sufficient Conditions for Stabilizability of Linear Periodic Differential Equations.

Phat, Vu Ngoc // Southeast Asian Bulletin of Mathematics; 2006, Vol. 30 Issue 2, p331This 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, p503We 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, p45We 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, p1698Consideration 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, p52By 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, p267In 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, p387This 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, p11In 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, p199Abstract. 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, p135This 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, p251Stability 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 p1An 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, p1565We 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, p012501We 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...

- Numerical solution of multiband kÂ·p model for tunnelling in type-II heterostructures.

Botha, A. E. // South African Journal of Science; Jul/Aug2009, Vol. 105 Issue 7/8, p294A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband kÂ·p description of the bulk energy-band structure, a multiband kÂ·p Riccati equation was derived. The reflection and...

- 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, p503The 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, p45The 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, p033505A 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, p323This 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, p445We 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 CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS ON THE SPACE OF SYMMETRIC MATRICES.

Dragan, Vasile; Freiling, Gerhard; Hochhaus, Andreas; Morozan, Toader // Electronic Journal of Differential Equations; 2004, Vol. 2004, p1In the first part of this paper we analyze the properties of the evolution operators of linear differential equations generating a positive evolution and provide a set of conditions which characterize the exponential stability of the zero solution, which extend the classical theory of Lyapunov....

- 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, p1Several 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, p1In 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...

- SPECIAL SOLUTIONS OF THE RICCATI EQUATION WITH APPLICATIONS TO THE GROSS-PITAEVSKII NONLINEAR PDE.

AL BASTAMI, ANAS; BELIĆ, MILIVOJ R.; PETROVIĆ, NIKOLA Z. // Electronic Journal of Differential Equations; 2010, Vol. 2010, Special section p1A method for finding solutions of the Riccati differential equation y' = P(x) + Q(x)y + R(x)yÂ² is introduced. Provided that certain relations exist between the coefficient P(x), Q(x) and R(x), the above equation can be solved in closed form. We determine the required relations and find the...

- The WKB method and differential consequences of the Riccati equation.

Chuprikov, N. L. // Mathematical Notes; Jun2011, Vol. 89 Issue 5/6, p885generalized 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, p933Functional representations of (matrix) Burgers and potential Kadomtsev-Petviashvili (pKP) hierarchies (and others), as well as some corresponding BÃ¤cklund transformations, can be obtained surprisingly simply from a â€œdiscreteâ€ 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, p1559Consideration 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, p1813Consideration 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, p293The 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, LamÃ©, Gauss, and Legendre.

- OSCILLATION CRITERIA FOR SEMILINEAR ELLIPTIC EQUATIONS WITH A DAMPING TERM IN â„n.

TADIE // Electronic Journal of Differential Equations; 2010, Vol. 2010, Special section p1We use a method based on Picone-type identities to find oscillation conditions for the equation n âˆ‘ ij=1 âˆ‚/âˆ‚xi (aij(x)âˆ‚/âˆ‚xj)u + f(x, u, âˆ‡u) + c(x)u = 0, with Dirichlet boundary conditions on bounded and unbounded domains. In this article, the above method...

- 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, p1426In 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, p557To 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, p557To 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...

âˆž-symmetries and nonlocal symmetries of exponential type.

MURIEL, C.; ROMERO, J. L. // IMA Journal of Applied Mathematics; Apr2007, Vol. 72 Issue 2, p191Nonlocal symmetries generated by type I hidden symmetries are identified as specific

âˆž-symmetries of an nth-order ordinary differential equation. The general method of reduction associated to these âˆž-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, p419This 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...

- MÃ¶bius Transformations and Periodic Solutions of Complex Riccati Equations.

Campos, Juan // Bulletin of the London Mathematical Society; 1997, Vol. 29 Issue 2, p205In this paper we are going to study the solutions of a complex T-periodic Riccati equation zâ€²=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...

- Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method.

Gómez S., Cesar A.; Salas, Alvaro H.; Frias, Bernardo Acevedo // Mathematical Problems in Engineering; 2010, Vol. 2010, Special section p1We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is...

- Matrix Bounds for the Solution of the Continuous Algebraic Riccati Equation.

Juan Zhang; Jianzhou Liu // Mathematical Problems in Engineering; 2010, Vol. 2010, Special section p1We propose new upper and lower matrix bounds for the solution of the continuous algebraic Riccati equation (CARE). In certain cases, these lower bounds improve and extend the previous results. Finally, we give a corresponding numerical example to illustrate the effectiveness of our results.

- 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 p1Pollution 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, p74We 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 LiÃ©nard Type Equations and Its Generalization.

Johnpillai, A. G.; Mahomed, F. M. // Applied Mathematics & Information Sciences; 2013, Vol. 7 Issue 6, p2355We study the linearization of a class of LiÃ©nard 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, p1341Many 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, p218In 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, p1By employing a generalized Riccati type transformation and the Taylor monomials, some new oscillation criteria for the even order functional dynamic equation (r(t)|xÎ”n-1 (t)|Î±-1 xÎ”n-1 (t)) Î” + F(t,x(t),x(Ï„(t)),xÎ” (t),xÎ” (Ï„(t))) = 0,tâˆˆ [t0, âˆž)T, are...

- Generalized Riccati equations for self-dual Yangâ€“Mills fields.

Chau, L.-L.; Yen, H. C. // Journal of Mathematical Physics; May87, Vol. 28 Issue 5, p1167It is shown that although no Riccati equations in the strict sense are likely to exist for the self-dual Yangâ€“Mills fields, certain â€˜â€˜generalized Riccati equationsâ€™â€™ derivable from the BÃ¤cklund 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, p531Consideration 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.

- On the local and nonlocal Camassaâ€“Holm hierarchies.

Casati, Paolo; Lorenzoni, Paolo; Ortenzi, Giovanni; Pedroni, Marco // Journal of Mathematical Physics; Apr2005, Vol. 46 Issue 4, p042704We construct the local and nonlocal conserved densities for the Camassaâ€“Holm equation by solving a suitable Riccati equation. We also define a Kadomtsevâ€“Petviashvili extension for the local Camassaâ€“Holm hierarchy.

- OSCILLATION OF SOLUTIONS TO IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES.

QIAOLUAN LI; FANG GUO // Electronic Journal of Differential Equations; 2009, Vol. 2009, Special section p1In 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 p1By 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,...