Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint

Abstract

In this paper, the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint. A new kind of mode-independent H∞ controller satisfying a minimum variance approximation is constructed, whose gain is composed of some mode-dependent control gains. The available probability of system mode is described by the Bernoulli variable and taken into account. It shows that such a probability plays an important role in system analysis and associates mode-independent controller with mode-dependent controllers. When the probability is unknown, a kind of adaptive controller is proposed such that the resulting closed-loop system is robust stochastically admissible with an H∞ performance. All the proposed conditions are given in terms of linear matrix inequalities. Two numerical examples are used to demonstrate the effectiveness of the proposed methods.