Stability and Disturbance Attenuation for Markov Jump Linear Systems with Time-Varying Transition Probabilities

Abstract

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being timeinhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.

Almost sure stability for a class of dual switching linear discrete‐time systems

“…Several stability concepts of stochastic systems, also applicable to Markov jump linear system, are defined such as the work of Ling and Deng, 12 where they investigate the δ moment stability of discrete‐time Markov jump linear systems with real rates, or the study on mean square stability 13 and the almost sure stability 14 . For more research results on the stability of Markov jump linear system, please refer to the prior art literature 15,16 . In recent years, the research of dual switching mainly focuses on the fixed dual switching system such as the work of Bolzern et al 17 on sufficient conditions of mean square stability, while in the study of Bolzern et al, 18 the almost sure stability of Markov jump linear systems with deterministic switching is investigated.…”

Almost surely attractive sets of discrete‐time Markov jump systems with stochastic disturbances via impulsive control

“…Moreover, Markov jump systems have found important applications in various fields, such as target tracking problems, networked control systems, sampled‐data control systems, fault‐tolerant systems and mechanical systems. Many significant results on the theory and application of Markov jump systems have been obtained, see [1–7].…”

Mean square stabilization of discrete‐time switching Markov jump linear systems

“…For MJLS, δ ‐moment stability implies AS stability, but not vice versa. For more results on the stability of MJLS, please refer to the works of Fang and Loparo and Lutz and Stilwell . In addition, some new extension of stability results on semi‐MJLS are also proposed …”

“…For more results on the stability of MJLS, please refer to the works of Fang and Loparo 17 and Lutz and Stilwell. 18 In addition, some new extension of stability results on semi-MJLS are also proposed. [19][20][21] Recently, a new switched system is proposed in which the switching of subsystem is dominated jointly by a deterministic rule and stochastic rule.…”