Contractive Sets of Discrete-Time Switched System with Mode-Dependent Persistent Dwell-Time Constraint

In this paper, we study the contractive set problem of discrete switching systems, where the switching signal is under the constraint of mode-dependent persistent dwell time (MD-PDT). Firstly, the stability condition of the MD-PDT switching sequence is given by the Quasi-time Lyapunov function method. Then the enumeration algorithm of the switching sequence is proposed, and the segmentation of the switching sequence is realized by using the cutting technique, which converts the set calculation problem of infinite sequence into a finite power calculation. Finally, an iterative algorithm for solving the MD-PDT contractive set under state constraints is given, and the related properties of the set are analyzed.