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Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics. (English) Zbl 1218.93089
Summary: This paper investigates the small-gain type conditions on Stochastic iISS (SiISS) systems and makes full use of these conditions in the design and analysis of the controller. The contributions are as follows: (1) A new proof of the stochastic LaSalle theorem is provided; (2) The small-gain type conditions on SiISS are developed and their relationship is discussed; (3) Based on the stochastic LaSalle theorem and SiISS small-gain type conditions, the adaptive controllers are designed to guarantee that all of the closed-loop signals are bounded almost surely and the stochastic closed-loop systems are globally (asymptotically) stable in probability.

MSC:
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
93E15 Stochastic stability in control theory
93C40 Adaptive control/observation systems
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