Discrete-time switching linear system with constraints: Characterization and computation of invariant sets under dwell-time consideration

Invariant Sets Analysis for Constrained Switching Systems

“…As it is the case with unconstrained systems [8], [25], [6], [16], we may establish convex approximations of the minimal convex invariant multi-set. We consider the multi-set sequences, {N…”

“…We call nominal the disturbance-free system, i.e., the system x(t + 1) = A σ(t) x(t) together with (2), (4)- (6). The stability of the nominal system is characterized by the constrained joint spectral radius [10] Assumption 1 (State constraints) The constraint sets…”

“…In interesting cases, switching is not arbitrary, see, e.g., dwell time and fault-detection settings [6]- [9]. Constrained switching can be described by labeled directed graphs [10]- [14].…”

“…[15], [16], of these systems is missing. Related studies include works on Markov Jump Linear Systems [17], dwell-time [6], [18], [19], periodic [20] and cyclic [21] invariance. In this article, we focus on how invariance 1 generalizes to constrained switching and develop the notion of invariant multi-sets.…”

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

“…Recently, by meas of the concept of contractive set, Dehghan and Ong proposed a necessary and sufficient asymptotic stability condition for (2.1) with a certain constraint (Dehghan & Ong, 2012); however, it is difficult to apply the method to systems with delays.…”