Absolute stabilization of switched Lurie systems with dwell time via dynamic output feedback

Abstract

In this article, we study the absolute stabilization of switched Lurie system via dynamic output feedback, where the nonlinearity is unknown and is restricted in a sector. In most works, the nonlinearity is assumed to be known exactly or is restricted in a bounded sector. Here, we consider the most general case with unbounded sector. With the help of switched time‐varying Lyapunov–Lurie function, a dynamic output feedback controller with time‐varying control gain is presented. On this basis, sufficient conditions for absolute stabilization are derived in the framework of mode‐dependent minimum dwell time and mode‐dependent range dwell time. It turns out that this time‐varying control strategy can solve the absolute stabilization of switched Lurie systems that all subsystems are not stabilizable. Moreover, the stability criteria in terms of linear matrix inequality we derived can be easily checked via Matlab toolbox. Finally, the effectiveness of presented methods is verified by several numerical examples.