Asynchronous control of switched Lurie systems with dwell time

In this paper, we study the absolute stability and H-infinity control problem for switched Lurie system (SLS) under asynchronous switching. A novel Lyapunov-Lurie function is constructed, which is discontinuous and allowed to increase at the switching instants and the instants when controller modes and system modes are matched. Considering the superiority of time-varying Lyapunov function technique, this paper is concerned with the Lyapunov-Lurie function with time-varying characteristic. Then, based on the switched time-varying Lyapunov-Lurie function (STVLLF) and mode-dependent minimum dwell time (MDMDT) method, some control synthesis conditions are derived. The developed controller can guarantee the absolute stability and L-2-gain performance for the closed-loop SLS with admissible switching lag. Subsequently, a time-varying control scheme is proposed from the STVLLF. H-infinity control synthesis conditions in terms of linear matrix inequalities are established, which improve the existing results. Finally, two numerical examples are considered to illustrate the effectiveness of the proposed approaches.