Switched systems with average dwell time: Computation of the robust positive invariant set

In this paper, computational results of robust positive invariant (RPI) sets for switched systems with amplitude bounded, persistent, additive disturbance and average dwell time (ADT) switching are developed. Towards this end, new idea for facilitating the analysis of the ADT switching signal is conceptualized by a series of predefined stages and sufficient conditions for the existence of an ADT RPI set of the considered systems are established. By utilizing the structure characteristics at each stage of the ADT switching signal, an exact computational algorithm of the ADT RPI set of the considered system is developed. The effectiveness of the proposed algorithms are illustrated by a numerical example.