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

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.