Stability of singularly perturbed switched systems with time delay and impulsive effects

H∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

“…In many SPSs, is usually a known physical parameter. Based on the fact that is available for feedback control, some synthesis problems are considered in [19,20,22]. In [22], for a given -bound 0 , under the dwell time switching law, the -dependent multiple Lyapunov function method was proposed to ensure exponential stability of the original switched system.…”

“…The control model of the hot strip mill was treated as a SPSS and an 2 robust controller was designed in [15]. Recently, SPSSs have attained much attention in the literature (see [16][17][18][19][20]). It has been shown in [17][18][19][20] that the stability of fast/slow switched subsystems can not guarantee the stability of the original switched systems.…”

“…These conditions were described by a few -dependent algebraic inequalities, which led to a heavy and tedious calculation. The proposed method in [19] was further extended to time-delay SPSSs with impulsive effects [20]. However, few results on the -bound estimation are available for SPSSs.…”

Exponential Stability of Uncertain Switched System with Time-Varying Delay

“…A switched systems is composed of a family of continuous time Alan & Lib, 2009Kim et al, 2006;Niamsup, 2008;Lien et al, 2009;Lib et al, 2008) or discrete time systems (Wu et al, 2004) and a switching condition determining at any time instant which subsystem is activated.…”

“…Switched system in which all subsystems are stable was studied in (Lien et al, 2009) and switched system in which subsystems are both stable and unstable was studied in Alan & Lib, 2009. The commonly used approach to stability analysis of switched systems is Lyapunov theory and some important preliminaries results have been applied to obtain sufficient conditions for stability of switched systems.…”