Finite time stability and L2-gain analysis for switched linear systems with state-dependent switching

Finite-time stability of switched nonlinear systems with finite-time unstable subsystems

“…Now, let us review the definition of finite-time stability and finite-time boundedness of the switched system (1) and (3) which are extended from the definitions proposed by Amato [25] and are extensively used in the references such as [37,38,[43][44][45][46]. Definition 1.…”

“…Recently, finite-time stability of switched systems has attracted much more attentions, but it should be pointed out that the potential assumption of most existing results is that each subsystem should be finite-time stable, such as [43][44][45][46]. If one subsystem of the switched systems is not finitetime stable, the results in those previously mentioned articles may not work.…”

“…In Theorems 1-4, it is not assumed that each subsystem of the switched system should be finite-time stable as that was potentially assumed in [35,[37][38][39][40][41][42][43][44][45][46]. If one subsystem of switched systems is not finite-time stable, the results in the previous references may not work, while the results in this note still work in some cases.…”

Finite‐time stability of switched linear systems with subsystems which are not finite‐time stable

“…Recently, finite-time stability problem of switched systems has attracted more and more attention, such as [20][21][22][23][24][25][26][27][28][29]. Based on the linear matrix inequalities (LMIs), finite-time stability and stabilisation conditions for the switched system without or with time-delay were developed in [22,27,30], respectively.…”

“…It should be pointed out that the potential assumption of most existing results, such as those in [20][21][22][26][27][28][29][30], is that each subsystem should be finite-time stable or finite-time bounded. If any one subsystem of the switched system is not finite-time stable or finite-time bounded, the results in the previous papers may not be true.…”