Observer-Based Passive Control Of Non-Homogeneous Markov Jump Systems With Random Communication Delays

This paper focuses on the passive control problem for Markov jump systems with piecewise-constant transition rates, random nonlinearities and random communication delays. An observer is used to obtain the system state, and communication delay with probabilistic distribution is considered. The probabilistic properties of the nonlinear perturbations and communication delays are described by two mutually independent Bernoulli sequences. Based on average dwell time method and Lyapunov stability theory, a sufficient stochastic passivity condition is presented. By singular value decomposition technique the gain matrices can be computed via strict linear matrix inequalities, and the desired controller guarantees the stochastic passivity of the closed-loop augmented system. The effectiveness of the method is illustrated by a numerical example.