Finite‐time
            <i>H</i>
            <sub>∞</sub>
            control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches

Luan, Xiaoli; Zhao, Changzhong; Liu, Fei

doi:10.1049/iet-cta.2013.0759

Cited by 17 publications

(8 citation statements)

References 35 publications

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“…An input‐output model by substituting a feedback interconnection formulation for the time‐delayed filtering error MJSs is proposed in the work of Wei et al Zhang et al use a mode‐dependent Lyapunov‐Krasovskii functional that includes tripe integrals term to provide the stability conditions. This result is further extended in the work of Luan et al, which studies the finite‐time

H_{\infty}

control subject to the average dwell‐time constraint for discrete case.…”

Section: Introductionmentioning

confidence: 68%

Sliding mode control of time‐varying delay Markov jump with quantized output

Zhang

Shen

2018

Optim Control Appl Methods

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This paper investigates the quantized sliding mode control of Markov jump systems with time-varying delay. A dynamical adjustment law is explored to quantize the system output. By constructing an observer-based integral sliding surface, a sliding mode controller is designed to take over the dynamical motion of state estimation and ensure the reachability of sliding surface. A new scaling manner is developed to build the bound between the system output and quantized error. With the help of separation strategies for controller synthesis and general transition probabilities and a lower bound theorem for nonlinear integral terms, a new synthesis method to ensure the required stability and meet the required  ∞ performance is proposed in the form of linear matrix inequalities. The validity of the proposed control method is illustrated by a numerical example. KEYWORDS ∞ control, Markov jump system, quantized control, sliding mode control INTRODUCTIONRecently, much attention has been devoted to the field of Markov jump systems (MJSs). This kind of system is extensively applied in many practical fields, such as flight control systems, network control systems, and manufacturing systems. Transition probabilities (TPs), which illustrate the possibility of switching among system modes, have direct impact on system behavior. By now, most of the existing results are assumed that they are known. However, this assumption is hard to be realized due to challenges like accuracy of measuring methods and environment conditions. 1 Hence, from the perspective of engineering applications, MJSs with general TPs are investigated in other works. [2][3][4][5][6] On the other hand, in physical processes, time delay is unavoidable and should be taken into account in the stage of controller design. 7 As a consequence, a dynamic output feedback control of MJSs with time delay is considered in the work of Boukas et al. 8 Xu et al 9 obtain a stochastic stability with the prescribed  ∞ performance via a bounded real lemma and slack matrix variables. An input-output model by substituting a feedback interconnection formulation for the time-delayed filtering error MJSs is proposed in the work of Wei et al. 10 Zhang et al 11 use a mode-dependent Lyapunov-Krasovskii functional that includes tripe integrals term to provide the stability conditions. This result is further extended in the work of Luan et al, 12 which studies the finite-time  ∞ control subject to the average dwell-time constraint for discrete case.Sliding mode control (SMC) is an effective measurement to deal with system uncertainties. This technique has been proved to have features such as fast response and insensitive to variations in internal and external disturbances. [13][14][15] Numerous achievements about SMC for stochastic system have been published, especially for MJSs; see other works [16][17][18][19][20][21][22] 226

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H_{\infty}

control subject to the average dwell‐time constraint for discrete case.…”

Section: Introductionmentioning

confidence: 68%

Sliding mode control of time‐varying delay Markov jump with quantized output

Zhang

Shen

2018

Optim Control Appl Methods

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“…A special case of the TVJRs is the time‐invariant JRs, which can be described as

normalΠ = ([], \begin{matrix} π_{11} & π_{12} & \dots & π_{1 s} \\ π_{21} & π_{22} & \dots & π_{2 s} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ π_{s 1} & π_{s 2} & \dots & π_{ss} \end{matrix}) .

Remark Note that in the system , the high‐level deterministic switching only affects the TVJRs, which is quite different from the SD‐MJLS , where the model is described by a combination of a finite number of linear subsystems indexed by both the deterministic switching signal and stochastic jumping process. Therefore, the system is able to depict a large number of time‐varying MJDSs with less complexity where only a single MJDS is considered.Remark The TVJR matrix is modeled by JRs subject to ADT constraint.…”

Section: System Description and Problem Formulationmentioning

confidence: 99%

“…Note that in the system (1), the high-level deterministic switching only affects the TVJRs, which is quite different from the SD-MJLS [9][10][11][29][30][31], where the model is described by a combination of a finite number of linear subsystems indexed by both the deterministic switching signal and stochastic jumping process. Therefore, the system (1) is able to depict a large number of timevarying MJDSs with less complexity where only a single MJDS is considered.…”

Section: Remarkmentioning

confidence: 99%

“…Note that the stochastic Lyapunov function (10), (29), and (19) can be employed to design modeindependent controller for common MJDS, switching controller for MJDS with time-invariant JRs, and switching controller for MJDS with TVJRs, respectively.…”

Section: Remarkmentioning

confidence: 99%

“…It is worth mentioning that the finite‐time switching control approach also reduces the design complexity of mode‐dependent and variation‐dependent controller synthesis developed for switching dynamics Markovian jump linear systems because the resulting controller only depends on the switching laws subject to ADT constraint. The usefulness of such a variation‐dependent but mode‐independent switching controller can be appreciated from the following two aspects.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite‐time stabilization of Markovian jump delay systems – a switching control approach

Wen

Nguang

Shi

et al. 2016

Intl J Robust & Nonlinear

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Summary In this paper, a finite‐time stabilization problem is considered for a class of continuous‐time Markovian jump delay systems (MJDSs). A switching controller, which only depends on the average dwell time (ADT) switching laws, is proposed to make a trade‐off between robustness and adaptiveness when the design complexity of mode‐independent, mode‐dependent, and mode‐dependent and variation‐dependent control strategies is considered. First, the stochastic finite‐time boundedness for an MJDS is analyzed by an ADT approach. Second, the disturbance attenuation capability of MJDS is studied via a finite‐time weighted L2 gain, which depends on the switching numbers. The impacts of finite‐time interval and L2 gain acting on the ADT are also thoroughly discussed. Then, a switching controller is designed such that the resulting closed‐loop MJDS is stochastically finite‐time bounded and has a guaranteed disturbance attenuation level. Finally, a numerical example is provided to verify the effectiveness of the developed results. Copyright © 2016 John Wiley & Sons, Ltd.

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Exponential stability for switched semi‐Markov jump systems with mode‐dependent average dwell time and generally uncertain transition rates

Liu,

2024

Asian Journal of Control

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This paper investigates the exponential stability in mean square sense for a class of stochastic switched semi‐Markov jump systems (ssSMJS). In this model, a hierarchical control switched regulation is designed, considering the external stochastic disturbances and generally uncertain transition rates (TRs) of the entire system and making the system more general and practical. By using appropriate Lyapunov–Krasovskii functional, linear matrix inequality, Jensen inequality, and mode‐dependent average dwell time (MDADT), sufficient conditions on the exponential stability in mean square sense for ssSMJS are derived. Furthermore, a nonfragile state feedback controller is designed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion.

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Finite‐time H _∞ control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches

Cited by 17 publications

References 35 publications

Sliding mode control of time‐varying delay Markov jump with quantized output

Sliding mode control of time‐varying delay Markov jump with quantized output

Finite‐time stabilization of Markovian jump delay systems – a switching control approach

Exponential stability for switched semi‐Markov jump systems with mode‐dependent average dwell time and generally uncertain transition rates

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Finite‐time H ∞ control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches

Cited by 17 publications

References 35 publications

Sliding mode control of time‐varying delay Markov jump with quantized output

Sliding mode control of time‐varying delay Markov jump with quantized output

Finite‐time stabilization of Markovian jump delay systems – a switching control approach

Exponential stability for switched semi‐Markov jump systems with mode‐dependent average dwell time and generally uncertain transition rates

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Finite‐time H _∞ control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches