Constraint admissible state sets for switched systems with average dwell time

The exact computational problem of lambda-constrained admissible average dwell time (CAADT) contractive set and CAADT invariant set for discrete-time switched systems with and without persistent amplitude bounded additive disturbance is investigated in this paper. The considered switching signal satisfies average dwell time (ADT) and is discussed in terms of stage which is both length-based and sequence based for the first time. Two more general criteria are established for checking the existence of the lambda-average dwell time (ADT) contractive set and the ADT invariant set of the considered system by assuming the value of stage length is taken from an arbitrary finite set. A detailed discussion is included to identify a proper value for stage length by taking the computational complexity and the conservatism of the designed finite-step computational algorithms of the lambda-CAADT contractive set and the CAADT invariant set into consideration. Some characteristics of the admissible lambda-CAADT contractive set and CAADT invariant set are derived. An illustrative example illustrates the effectiveness of the developed results. (C) 2017 Elsevier Ltd. All rights reserved.