Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

Tanelli, Mara; Picasso, Bruno; Bolzern, Paolo; Colaneri, Patrizio

doi:10.1109/tac.2009.2033844

Cited by 58 publications

(23 citation statements)

References 20 publications

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“…For instance, the precision requirement in the rocket control problem should be guaranteed with the probability 1. Therefore, the almost sure stability [22], [23], which describes the system performance from the viewpoint of system sample paths, has recently attracted considerable attention, see [4], [16], [17], [29] and the references therein. Up to now, the corresponding results mainly involve the performance analysis of input-to-state stability and stochastic stability in almost sure sense, and the controller structure is mostly dependent on state/output feedback.…”

Section: Introductionmentioning

confidence: 99%

Almost sure H ∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

et al. 2016

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This paper investigates the almost sure H ∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stability and the H ∞ performance of the system dynamics in the specified sliding surface. A SMC law is designed to guarantee the reachability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme.

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Section: Introductionmentioning

confidence: 99%

Almost sure H ∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

et al. 2016

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“…For example, the performance requirement of the controlled rocket should be guaranteed with the probability 1. Very recently, the analysis and design problems in almost sure sense have attracted considerable attention, see [3,4,13,14,30] and the references therein. For instance, a Razumikhin-type theorem on pth moment input-to-state stability has been developed in [14] for a class of nonlinear stochastic systems with Markovian switching.…”

Section: Introductionmentioning

confidence: 99%

Almost sure state estimation withH2-type performance constraints for nonlinear hybrid stochastic systems

Yang

Shu

Wang

et al. 2016

Nonlinear Analysis: Hybrid Systems

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This paper is concerned with the problem of almost sure state estimation for general nonlinear hybrid stochastic systems whose coefficients only satisfy local Lipschitz conditions. By utilizing the stopping time method combined with martingale inequalities, a theoretical framework is established for analyzing the so-called almost surely asymptotic stability of the addressed system. Within such a theoretical framework, some sufficient conditions are derived under which the estimation dynamics is almost sure asymptotically stable and the upper bound of estimation error is also determined. Furthermore, a suboptimal state estimator is obtained by solving an optimization problem in the H 2 sense. According to the obtained results, for a class of special nonlinear hybrid stochastic systems, the corresponding conditions reduce to a set of matrix inequalities for the purpose of easy implementation. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the results derived.

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“…RSS have been suggested as a suitable modeling paradigm in diverse areas such as finance, population dynamics, manufacturing, and fault-tolerant control (Cassandras & Lygeros, 2007). Stability of Markov Jump Linear Systems (MJLS), is studied in Bolzern, Colaneri, and De Nicolao (2006), Feng, Loparo, Ji, and Chizeck (1992) and Tanelli, Bolzern, and Colaneri (2010), as a special case of RSS in which dynamics are given by ordinary linear differential equations, and the switching process is a continuous time Markov chain with a discrete state space. Stability in the more general case of Switched Diffusion Processes (SDP), where process noise is represented through a Wiener process, is studied in Yuan and Mao (2003).…”

Section: Introductionmentioning

confidence: 99%

Stochastic stability of systems with semi-Markovian switching

2014

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Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

Cited by 58 publications

References 20 publications

Almost sure H ∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

Almost sure H ∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

Almost sure state estimation withH2-type performance constraints for nonlinear hybrid stochastic systems

Stochastic stability of systems with semi-Markovian switching

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