Maximal admissible set for graph-dependent switched systems with dwell time restriction
Résumé
In this paper we present an extension of the concept of the maximal admissible set for constrained graph-dependent switched systems with bounded disturbances under dwell time restriction. Termed as the maximal switch-dependently robustly admissible set (MSDRAS), we provide efficient numerical procedures for its determination. For this purpose, we exploit available information about the current active mode, minimum dwell times, and mode transition graph. We employ the MSDRAS for three purposes: i) characterizing the largest set of initial states ensuring constraint satisfaction; ii) establishing necessary and sufficient conditions for stability of switched systems; iii) computing the minimum mode-dependent dwell times. Furthermore, we extend the results to switched systems with parametric uncertainties. Through three numerical examples, we compare our solutions with earlier from the literature to illustrate the effectiveness of our approach.
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