Exponential stability of some interconnected stochastic control systems with non-trivial equilibria

Abedi, Fakhreddin; Leong, Wah June; Shahemabadi, Ali Rafiei

doi:10.1016/j.ejcon.2020.08.011

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Subsequently, the almost sure exponential stability was extended to nonlinear systems in [3]. In addition, other good results are available in [4][5][6][7][8]. However, in the current literature, the exponential stability has been analyzed mainly considering the steady-state behavior without considering the transient behavior.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises

et al. 2022

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In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example.

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