Constraint admissible state sets for switched systems with average dwell time

The exact computational problem of λ-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 λ-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 λ-CAADT contractive set and the CAADT invariant set into consideration. Some characteristics of the admissible λ-CAADT contractive set and CAADT invariant set are derived. An illustrative example illustrates the effectiveness of the developed results.