H∞ performance analysis of delayed nonlinear Markov jump systems with piecewise-constant transition rates

Abstract

This paper is concerned with the problem of H∞ performance analysis for delayed nonlinear Markov jump systems with piecewise-constant transition rates. The delays and nonlinearities are randomly occurring in a probabilistic way, described by Bernoulli sequences. The transition rates are time-varying and subject to the average dwell time switching. The sufficient stochastic stability condition is established based on average dwell time switching approach and Lyapunov functional method. The sufficient condition ensuring the system has a guaranteed H∞ noise-attenuation performance index is presented. A numerical example is presented to demonstrate the validity of the method.