Control design of non‐homogeneous Markovian jump systems via relaxation of bilinear time‐varying matrix inequalities

Abstract

This study addresses the issue of control synthesis for discrete-time non-homogeneous Markov jump systems. Here, the concept of multiple boundary sets (BSs) is made to represent time-varying transition probabilities of the system operation mode, and another kind of probabilities is exploited to describe the switching among the multiple BSs. Overall, the H ∞ stabilisation condition is first derived in terms of bilinear time-varying matrix inequalities with two kinds of probabilities that affect the evolvement of the modes. Then, to derive a finite number of solvable conditions from the stabilisation condition, this study introduces a relaxation technique capable of directly integrating some available constraints on the probabilities without resorting to any over-bounding technique.