On uniform exponential stability of linear switching system

Abstract

We prove that the linear switching system wfalse(n+1false)=Aϑfalse(nfalse)wfalse(nfalse), where Aϑfalse(nfalse) is bounded valued square matrices and ϑ:[0,1,2,…)→Ω is an arbitrary switching signals, is uniformly exponentially stable if the sequence n↦true∑k=1nAϑfalse(n−1false)Aϑfalse(n−2false)⋯Aϑfalse(kfalse)sfalse(kfalse) is bounded, where s(k) is bounded valued sequence.

β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

“…Different researchers are working to discuss stability analysis of different systems using evolution family. For more details of evolution family we prefer [20,28,[37][38][39][40][41][42][43][44].…”

Input distinguishability of linear dynamic control systems

“…The switched system is an important case of a hybrid system. As a special kind of linear switched systems has been extensively investigated [1][2][3][4][5]. When we consider the observability of switched systems composed by time-invariant subsystems, distinguishability plays a crucial role (see [6]).…”