New bounded real lemma for singular Markovian jump systems: Application to H∞ control

Abstract

This article proposes a new strictly bounded real lemma (BRL) for continuous-time singular Markovian jump systems (SMJSs) in terms of strict linear matrix inequalities (LMIs). While the previous studies have been done for SMJSs that do not have a path from disturbances to desired output, the proposed BRL covers SMJSs with disturbance-contaminated output by introducing additional free matrix variables. Based on the proposed BRL, the sufficient condition for state-feedback stabilization is successfully obtained in terms of strict LMIs. The result leads to find the minimal (Formula presented.) performance by solving the optimization problem subject to the suggested LMIs. Two examples show the less conservatism of proposed method compared with the previous work. ? 2020 John Wiley & Sons, Ltd.