State-feedback stabilization of discrete-time switched linear systems with improved PDT constraints

This paper is concerned with the issues of stability analysis and state-feedback stabilization control design for a class of discrete-time switched linear systems. Other than the existing studies on the persistent dwell time (PDT) switching signals, the average dwell time (ADT) switching property is considered together with the PDT switching constraint here to eliminate the restriction of dwell time requirements and to lift the flexibility of PDT switching signals design. By virtue of the semi-time-varying (STV) Lyapunov function approach, the stability criteria are derived for the considered system. Then sufficient conditions on the solvability of stabilizing controllers in STV form are obtained, and the corresponding controller gains are calculated by solving a cluster of linear matrix inequalities. Finally, the advantage of the developed theoretical results is illustrated via a numerical example.