Controller Design for Switched LPV Systems with Hidden semi-Markov Mode Switching

Abstract

This paper is concerned with issue of stability analysis and control synthesis for a class of switched LPV systems with stochastic mode switching. The stochastic switching process is further regarded as hidden semi-Markov switching by using concepts of semi-Markov kernel and emission probability. With the construction of a novel Lyapunov function that depends on accessible-mode, parameter as well as elapsed time, the mean-square stability (MSS) criteria are developed for the closed-loop system with the usage of designed controller. Numerically testable stability criteria are established in sense of MSS by introducing the upper bound sojourn time and some mathematical techniques. The theoretical results are testified by a numerical example to demonstrate the effectiveness of the designed stabilizing controller.