Brief paper: Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics

Authors:
Xin Yu;Xue-Jun Xie;Na Duan
Affiliations:
School of Automation, Southeast University, Nanjing, Jiangsu Province, 210096, China and Institute of Automation, Qufu Normal University, Qufu, Shandong Province, 273165, China;Institute of Automation, Qufu Normal University, Qufu, Shandong Province, 273165, China;School of Electrical Engineering and Automation, Xuzhou Normal University, Xuzhou, Jiangsu Province, 221116, China and Institute of Automation, Qufu Normal University, Qufu, Shandong Province, 273 ...
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

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.