TY - JOUR
T1 - Windows of opportunity for the stability of jump linear systems
T2 - Almost sure versus moment convergence
AU - Porfiri, Maurizio
AU - Jeter, Russell
AU - Belykh, Igor
N1 - Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2019/2
Y1 - 2019/2
N2 - In this paper, we examine the role of the switching period on the stochastic stability of jump linear systems. More specifically, we consider a jump linear system in which the state matrix switches every m time steps randomly within a finite set of realizations, without a memory of past switching instances. Through the computation of the Lyapunov exponents, we study δ-moment and almost sure stability of the system. For scalar systems, we demonstrate that almost sure stability is independent of m, while δ-moment stability can be modulated through the selection of the switching period. For higher-dimensional problems, we discover a richer influence of m on stochastic stability, quantified in an almost sure and a δ-moment sense. Through the detailed analysis of an archetypical two-dimensional problem, we illustrate the existence of disconnected windows of opportunity where the system is asymptotically stable. Outside of these windows, the system is unstable, even though it switches between two Schur-stable state matrices.
AB - In this paper, we examine the role of the switching period on the stochastic stability of jump linear systems. More specifically, we consider a jump linear system in which the state matrix switches every m time steps randomly within a finite set of realizations, without a memory of past switching instances. Through the computation of the Lyapunov exponents, we study δ-moment and almost sure stability of the system. For scalar systems, we demonstrate that almost sure stability is independent of m, while δ-moment stability can be modulated through the selection of the switching period. For higher-dimensional problems, we discover a richer influence of m on stochastic stability, quantified in an almost sure and a δ-moment sense. Through the detailed analysis of an archetypical two-dimensional problem, we illustrate the existence of disconnected windows of opportunity where the system is asymptotically stable. Outside of these windows, the system is unstable, even though it switches between two Schur-stable state matrices.
KW - Discrete-time
KW - Linear stochastic systems
KW - Lyapunov exponent
KW - Mean-square
KW - Stability
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U2 - 10.1016/j.automatica.2018.11.028
DO - 10.1016/j.automatica.2018.11.028
M3 - Article
AN - SCOPUS:85057828144
SN - 0005-1098
VL - 100
SP - 323
EP - 329
JO - Automatica
JF - Automatica
ER -