On Designing of Sliding-Mode Control for Stochastic Jump Systems

Shi, Peng; Xia, Yuanqing; Liu, Shuai; Rees, D.

doi:10.1109/tac.2005.861716

Cited by 611 publications

(262 citation statements)

References 25 publications

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“…MJSs are also appropriate and reasonable to describe systems subject to abrupt variation in their structures or parameters, which caused by failures of subsystems, sudden environmental changes, and system noises. It is a fact that transition probability plays an important role in the performance of such systems, under the assumption that the transition probabilities of MJSs are time invariant, some problems have been studied, such as system analysis [2,3], stochastic stability and stabilization [4], control [5][6][7][8][9][10][11][12], fault detection and filtering [13][14][15][16][17], fault tolerant and estimation [18,19] etc. Some work has also been done on systems with partially known or uncertain transition probability (see, e.g., [20][21][22][23][24] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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SUMMARYThis paper considers the problem of observer‐based H ∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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“…Among this work, T-S fuzzy systems and Markovian jump systems are two representative classes of dynamical systems. Over the past decades, many meaningful results have been published on the sliding mode control of either T-S fuzzy systems [10,11,12,13] or Markovian jump systems [14,15,16,17,18,19,20]. However, relatively little attention has been focused on research into sliding mode control for composite systems comprising the two classes of systems, namely Markovian jump T-S fuzzy systems [21,22], despite their wide application [23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Zhang

Yan

et al. 2017

IET Control Theory & Applications

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This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed.

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“…For example, In [25], a special integral-type switching function is constructed to guarantee that the system dynamics lies on the specified sliding surface. Very recently, the SMC problem of Markovian jump systems (MJSs) has gained particular research interests because of their practical applications in a variety of areas [5], [6], [19], [20], [28], [33]. The main reason could be that MJSs are very appropriate to model the dynamic systems whose structures are subject to random abrupt variation [26], [27].…”

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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On Designing of Sliding-Mode Control for Stochastic Jump Systems

Cited by 611 publications

References 25 publications

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

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

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On Designing of Sliding-Mode Control for Stochastic Jump Systems

Cited by 611 publications

References 25 publications

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

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

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Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input