Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities

Song, Jun; Niu, Yugang; Zou, Yuanyuan

doi:10.1016/j.automatica.2018.03.037

Cited by 167 publications

(69 citation statements)

References 28 publications

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“…(1)-(2) with the round-robin protocol (4)- (5). Let the matrix F in sliding function (8) and the parameter in the token-dependent SMC law (11) be given. If there exist matrices K (k) ∈ R m×p , P (k) > 0, Q (k) > 0, and scalars (k) > 0, (k), (k + 1) > 0, (k), (k + 1) > 0 such that the following matrix inequalities…”

Section: Analysis Of the Asymptotic Stabilitymentioning

confidence: 99%

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Static output‐feedback sliding mode control under round‐robin protocol

Song

Wang

Niu

2018

Intl J Robust & Nonlinear

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Summary This paper addresses the static output‐feedback sliding mode control (SMC) problem for a class of uncertain control systems subject to the round‐robin protocol scheduling, in which the communication between the controller and the actuators is regulated by the round‐robin protocol, that is, only one actuator node gets the access to the transmission network at each instant and the other actuators utilize the values stored in the zero‐order holders. A key issue of the addressed problem is how to design both the sliding surface and the sliding mode controller subject to the kind of actuator signals depending on protocol scheduling and zero‐order holders. By only using the measured output information, a linear sliding surface is constructed, and then, a token‐dependent SMC law is designed properly with the aid of an updating rule on actuator input. Moreover, suitable token‐dependent Lyapunov functions are exploited to obtain sufficient conditions for guaranteeing the asymptotic stability of the closed‐loop systems and the reachability of the specified sliding surface. Furthermore, based upon a separation strategy, a convex optimization algorithm is proposed to obtain the controller gains. Finally, the effectiveness of the developed static output‐feedback SMC design scheme is verified in an industrial continuous‐stirred tank reactor system.

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Section: Analysis Of the Asymptotic Stabilitymentioning

confidence: 99%

“…This section analyzes the reachability of the specified sliding surface (8). More specifically, by exploiting a token-dependent Lyapunov function, a sufficient condition will be derived to ensure that the state trajectories of the SMC system (13) enter into a sliding domain Ω around the specified sliding surface (8).…”

Section: Analysis Of the Reachabilitymentioning

confidence: 99%

Static output‐feedback sliding mode control under round‐robin protocol

Song

Wang

Niu

2018

Intl J Robust & Nonlinear

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“…In the work of Costa et al, it is discussed that the aforementioned mode‐dependent, cluster, and mode‐independent cases can be obtained from the detector approach framework, and also that the observed variable

\overset{θ}{true} false(k false)

could be viewed as a failure detector . This model is also known as asynchronous control as presented by Song et al in which the problems of static output feedback control and sliding mode control of MJLS with hidden observations were considered. Alternatively, Ogura et al considered an observation process in which the Markov chain is accessed only when some modes of operation of a different Markov process are visited.…”

Section: Introductionmentioning

confidence: 99%

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

Oliveira

Costa

2019

Intl J Robust & Nonlinear

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Summary The scriptH2, scriptH∞ and mixed scriptH2false/scriptH∞ dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable trueθ^false(kfalse) coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.

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“…On the other hand, Markovian jump systems (MJSs) is effective on modeling various psychical systems whose parameters and/or structure may stochastically abruptly change. Nowadays, it have been extensively applied to describe many practical systems, such as robot systems, economic systems, circuit systems, and so on . Due to their great application potential in engineering, much effort has been focused on solving the stability and stabilization problem of MJSs during the past decades .…”

Section: Introductionmentioning

confidence: 99%

“…Nowadays, it have been extensively applied to describe many practical systems, such as robot systems, economic systems, circuit systems, and so on. [18][19][20][21][22] Due to their great application potential in engineering, much effort has been focused on solving the stability and stabilization problem of MJSs during the past decades. [23][24][25] Moreover, a great number of researchers' interesting has been attracted to address the FTC problems for MJSs through SMC, and some related results have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Asynchronous adaptive output feedback sliding mode control for Takagi‐Sugeno fuzzy Markovian jump systems with actuator faults

Liu

Zhang

et al. 2019

Adaptive Control & Signal

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Summary In this article, the problem of asynchronous adaptive dynamic output feedback sliding mode control (SMC) for a class of Takagi‐Sugeno (T‐S) fuzzy Markovian jump systems (MJSs) with actuator faults is investigated. The asynchronous dynamic output feedback control strategy is employed, as the nonsynchronization phenomenon of jump modes exists between the plant and the controller. A novel asynchronous adaptive SMC approach is proposed to solve the synthesis problem for T‐S fuzzy MJSs with actuator faults. Sufficient conditions for stochastic asymptotic stability of T‐S fuzzy MJSs are given. Under the designed asynchronous adaptive SMC scheme, the effects of actuator faults and external disturbance can be completely compensated and the reachability of sliding surface is ensured. Finally, an example is provided to demonstrate the effectiveness of the proposed design techniques.

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Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities

Cited by 167 publications

References 28 publications

Static output‐feedback sliding mode control under round‐robin protocol

Static output‐feedback sliding mode control under round‐robin protocol

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

Asynchronous adaptive output feedback sliding mode control for Takagi‐Sugeno fuzzy Markovian jump systems with actuator faults

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