Observer-based Stabilization of Uncertain Switched Linear Systems with Admissible Edge-dependent Switching Signals

This paper focuses on the stabilization of a class of uncertain switched linear systems with admissible edge-dependent (AED) switching signals, where disturbances exist in not only the state equation but also output equation. The performance of switchings from the current system mode to the other is shown by the concept of admissible transition edge-dependent weights (ATEWs). A special output transformation is adopted to construct a new system with the same states as the original system but different output, where the disturbance in measurement equation is decoupled. Then, a multiple-mode unknown input observer (UIO) with AED switching is proposed to simultaneously estimate the state and disturbance. Next, an observer-based controller is developed to stabilize the uncertain switched system, then the conditions ensuring the stability of the closed-loop system are provided. Finally, the validity of the proposed method is shown by an example.