Stochastically switched control systems

Allison, Andrew; Abbott, Derek
March 2000
AIP Conference Proceedings;2000, Vol. 511 Issue 1, p249
Academic Journal
Stability is a global property of a system. It is concerned with the behavior of whole systems over indefinitely long periods of time, for all admissible inputs and uncertainties. Stability and instability are ultimately topological properties. They depend on the topology of the space defined by the equations that govern the system. It follows that that instability is not linear. It is possible to construct a linear combination of two unstable systems which will be stable. The operation of linear combination can be performed using time averaging. The switching can be periodic or stochastic. In the stochastic case, the variance plays an important role. It is possible to drive a system into instability by making the variance sufficiently large. The behavior near the limit of stability is quite complex, even for very simple “toy” systems. The stochastically switched system is not the same as a stationary linear filter, although we show that the power spectral densities of the two systems can appear to be very similar. We show that variation in the strength of a feedback loop is a new mechanism introducing noise into a system. © 2000 American Institute of Physics.


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