Stabilizabiltty of certain stochastic systems

Abstract

In this paper, we present certain sufficient conditions for (feedback) stabilizability of controlled stochastic systems. Theoretical results are illustrated by three examples applied to electrically suspended gyros.

Stability and stabilizability of stochastic evolution equations on Hilbert spaces

“…Another technique to convert the stochastic control problem to a deterministic control problem has been discussed byMahalanbis and Purkayastha (1973) and Gao and Ahmed ( 1986) in finite dimensions. Without a finite rank assumption on D i , i !i:; I, we state the following proposition.…”

“…Wonham (1974), Haussmann (1971Haussmann ( ,1973, and Willems and Willems (1976) have considered the related problem of the stabilizability of stochastic systems with state-and control-dependent noise in finite dimensions. In Mahalanbis and Purkayastha (1973) and Gao and Ahmed (1986), analogous problems have been discussed for Lure-type non-linear stochastic systems. For various results on the stability and stabilizability of linear stochastic systems with state-and control-dependent noise in finite dimensions, we refer to the J. H. Seo survey paper by Mohler and Kolodziej (1980).…”

Robustness of exponential stability of nonlinear stochastic systems

“…It should be noted that the robustness problem of linear and nonlinear stochastic system has received a good deal attention (see for instance [3], [4], [5], [6], [7], [8], [13] and [15]). For example, in order to derive a class of feedback controllers sufficient conditions based on the properties of the solution of an algebraic Riccati equation are provided in [15].…”

Controller synthesis for stochastic systems with persistent noise via semi-definite programming

“…Similarly important is the controller synthesis problem of stochastic systems. Among the early attempts based on solutions of algebraic Riccati equations, one can cite [5], [6]. Inspired by the advances in methods using control Lyapunov functions [7] and constructive Lyapunov stabilization [8] for nonlinear deterministic systems, researchers turned to controller synthesis algorithms for SDEs using stochastic control Lyapunov functions [9].…”