Constrained control of uncertain nonhomogeneous Markovian jump systems. (1st March 2017)

• Record Type: Journal Article
• Authors: Yin, Yanyan; Lin, Zongli
• Is Part Of: International journal of robust and nonlinear control. Volume 27:Number 17(2017)
• Page Start: 3937
• Page End: 3950
• Publication Date: 2017-03-01
• Subjects: nonlinear systems -- applications -- stabilization -- robust control -- actuator saturation -- Markovian jumps -- time‐varying transition probabilities -- uncertainties; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3774
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time‐varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time‐varying transition probabilities inside a polytope, we establish conditions under which the closed‐loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd.