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

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 Script capital H-infinity 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.