Modal and transition dwell time computation in switching systems: A set-theoretic approach

Abstract

We consider a plant the dynamics of which switch among a family of systems. Each of these systems has a single stable equilibrium point. We assume that a constraint region for the state is assigned and we consider the problem of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell times which lead to the definition of a dwell time vector and dwell time graph (represented by a proper matrix), respectively. The former imposes a minimum permanence on a discrete mode before commuting, the latter imposes the minimum permanence time on the current mode before switching to a specific new one. Both dwell time vector and dwell time graph, can be computed via set theoretic techniques. When the systems share a single equilibrium state, stability can be assured as a special case. Finally, under the assumption of affine dynamics, non-conservative values are achieved.

Stabilization and reference tracking for constrained switching systems: A predictive control approach

“…In this section, the effectiveness of the proposed SCTUS-A scheme will be investigated by considering the circuit depicted in Figure 4 and detailed in the work of Blanchini et al 8 Specifically, switch devices (positions (a) and (b) in Figure 4) and time-varying resistors R 1,2 and R 3,4 (summarized as follows) give rise to 4 LTI models:…”

“…5 This has first lead to the well-known concept of dwell time: for a given plant structure, the dwell time characterizes the minimum time of permanence in a system mode that ensures stability under switching events. 6 Further extensions of such a concept can be found in the works of Hespanha and Morse 7 and Blanchini et al, 8 where average and transition dwell times were respectively introduced.…”

“…switching instants; then, the class of systems(3)with σ(·) subject to a transition dwell time T i, j < ∞ (see the work of Blanchini et al8 ) …”

A Condition for Boundedness of Solutions of Bidimensional Switched Affine Systems With Multiple Foci and Centers

“…For switched systems with USs sharing a same equilibrium point, there are some stability/stabilization results obtained in [4,6,[13][14][15][16]. As for switched systems with all multiple stable equilibria, there are several stability/design results in [17][18][19][20][21][22][23][24][25]. Some results of boundedness and an invariant region of solutions are proposed for switched nonlinear systems with multiple equilibria via a set-theoretic approach in [18].…”

Stability analysis of switched linear systems defined by graphs

“…We consider a switched discrete time linear system that consists of four subsystems, i.e, A := {A i } i∈N [1,4] , where A 1 = Figure 4, where V := {i} i∈N [1,8] and E := {(1, 2), (2, 3), (2,4), (3,4), (4, 1), (4,5), (5,4), (5,5), (5,6), (6, 7), (7, 7), (7,8), (8,5) Figure 4 in green and red color. The in-neighbor sets (4) I i , i ∈ N [1,8] are I 1 = {4, 8}, I 2 = {1}, I 3 = {2}, I 4 = {1, 2, 3, 5}, I 5 = {4, 5, 8}, I 6 = {5}, I 7 = {6, 7}, I 8 = {7}.…”