Passivity‐based stochastic sampled‐data control of Markovian jump systems via looped‐functional approach

Abstract

Abstract In this article, passivity‐based sampled‐data control for Markovian jump systems (MJSs) with stochastic sampling is conducted by virtue of the looped‐functional approach. First, based on the input delay approach, the MJS under stochastic sampled‐data control is modeled as a time‐varying continuous‐time system with a random variable. Second, a time‐dependent looped‐functional is developed, which only requires its positive definiteness at the sampling instants and takes full use of the state information. Moreover, a free‐matrix‐based integral inequality is used to derive some less conservative passivity conditions expressed in terms of linear matrix inequality (LMIs). Meanwhile, a design algorithm for the mode‐dependent stochastic sampled‐data controller is provided. A numerical example is given to demonstrate the validity and superiority of the proposed analysis method.