Mixed Incremental <italic>H</italic>_&#x221E; and Incremental Passivity Analysis for Markov Switched Stochastic Nonlinear Systems

Abstract

This paper introduces the mixed incremental $H_\infty $ and incremental passivity control problem for Markov switched stochastic (MSS) nonlinear systems. The multiple incremental Lyapunov functions approach and the structure of Markov framework are utilized to establish some sufficient conditions for the MSS nonlinear systems, which will be used for the incrementally globally asymptotically stable in the mean(IGASiM) and performance index analysis. It is proved that under the proposed non-IGASiM subsystems the underlying MSS nonlinear systems are IGASiM and possess the mixed incremental $H_\infty $ and incremental passivity performance metric in the presence of specified conditions. The mathematical induction method is selected to guarantee the robust incremental stability of MSS systems with IGASiM and non-IGASiM subsystems and the performance index can be exhibited a prescribed decay rate. The effectiveness of the proposed results is demonstrated by two simulation examples.

Keywords

• Markov switched stochastic systems
• incrementally globally asymptotically stable
• nonlinear performance