Stabilization of two dimensional switched systems with unstable modes based on the weighted average dwell time strategy

This study focuses on the stabilization of two-dimensional (2-D) switched systems utilizing the Fornasini-Marchesini local state-space model. Without any controller, by designing a set of switching signals subject to weighted average dwell time approach, the 2-D switched systems with all subsystems unstable could be stabilized. The weighted average dwell time approach used in this paper is more effective than mode-dependent dwell time and average dwell time used in other literature. Furthermore, the introduction of a quasi-time-dependent Lyapunov functional ensures the asymptotically stability of the 2-D switched system. This paper addresses the stabilization challenges of 2-D switched systems by employing Fornasini-Marchesini local state-space model, offering a comprehensive approach to a field that is critical to both academic and industrial domains. The efficacy of these methodologies are demonstrated through an illustrative example.