Finite-time stability for continuous-time switched systems in the presence of impulse effects

Abstract

The problem of finite-time stability for a class of continuous-time switched systems with impulse effects is studied in this article. A criterion is proposed which ensures that the system's state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if the authors give a bound on the initial condition. Contrary to the existing results on finite-time stability of switched systems, the average dwell time approach, rather than the Lyapunov-based ones, is utilised to realise such a purpose. The difference between the finite-time stability and the Lyapunov stability is clearly shown. A numerical example is given to illustrate the proposed design method.

Finite‐time H ∞ control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches

“…Proposition 2: For given scalars δ ≥ 1, μ > 1 and γ > 0, the discrete-time switching MJLS (5) with time-delay is stochastic FTB and H ∞ finite-time stabilisable with respect to (c 1 c 2 N R h γ ), if there exists a set of positive-definite matrices P α,i > 0, α ∈ M, i ∈ S and positive-definite matrices Q such that the following inequalities hold (see (23))P α,i ≤ δP β,i (24) μ N γ 2 h 2 < c 2 2 min α∈M,i∈S λ min (P α,i ) (25) with average dwell time satisfying…”

“…Therefore the definition of finite-time stability (FTS) was proposed by Dorato [15] and the concept of FTS has been further extended to finite-time boundedness (FTB) [16,17] when system possesses bounded exogenous disturbance. A linear matrix inequality (LMI) framework has been established to distinguish FTS and LAS [18][19][20][21][22][23][24][25][26]. Compared with LAS condition from energy point of view, FTS relaxes the condition by allowing Lyapunov-like function to increase at every sampling time instant, which leads to less conservative results.…”

Non-uniform sampling finite-time control for networked control systems via event-driven transmission

“…17 So far, some attempts on the finite-time control have been conducted. [18][19][20][21][22][23][24][25] However, to the best of authors' knowledge, no results for utilizing the event-driven communication scheme are reported in the finite-time control sense, which motivates us for this study.…”

DDI-based finite-time stability analysis for nonlinear switched systems with time-varying delays

“…Furthermore, in these literatures, it is shown that FTS of each subsystem is necessary for FTS of the switched system, which leads to quite conservative results on the FTS analysis problem. In Wang, Shi, Wang, and Zuo (2012), the authors discussed the FTS property of switched linear systems in the presence of impulse effects by using the average dwell time approach rather than the Lyapunov-based ones. Some sufficient conditions, which dealt with different situations in which different information about the switching signal was known, were provided in Xiang and Xiao (2013) for FTS and boundedness of switched linear systems.…”

“…FTS and finite-time boundedness of switched linear systems with subsystems which are not finite-time stable or finite-time bounded were investigated in Lin, Li, and Zou (2014). While the results obtained in Wang et al (2012), Xiang and Xiao (2013), and Lin et al (2014) are very encouraging, time-delay is not considered in them.…”