Passivity and passification for switching Markovian jump systems with time‐varying delay and generally uncertain transition rates

Qi, Wenhai; Gao, Xianwen; Kao, Yonggui

doi:10.1049/iet-cta.2015.0726

Cited by 16 publications

(8 citation statements)

References 46 publications

(59 reference statements)

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“…And the passivity theory is an effective tool to study the stability of nonlinear or uncertain systems, especially for high-order systems. 41 Therefore, many results for the passivity and the passification of singular systems have been available in recent literatures (eg, References 43,44,46,51,and 52). In this article, we prepare to study the admissibility and the passivity of our considered system.…”

Section: Introductionmentioning

confidence: 99%

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Liu

et al. 2020

Intl J Robust & Nonlinear

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This article addresses the passivity analysis and passification problems for a class of nonlinear singular time-varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to "left-singular" form uncertainty in the derivative matrix (ie, E 0 (I + ΔE 0 ())). Next, an integral-type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov-Krasovskii functional and introducing slack matrix approach, in which the slack matrixW is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay-dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite-time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Liu

et al. 2020

Intl J Robust & Nonlinear

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“…D Uring the past few decades, switched systems, one special class of hybrid systems, have been widely investigated and many useful results have been obtained (see, for example [1][2][3][4][5][6][7]). If the data of a switched system is transmitted through the network, then the controller design will subject to the effect of quantization (caused by limited communication rate), delay and packet loss (caused by network congestion).…”

Section: Introductionmentioning

confidence: 99%

Event-Driven Control for Switched Systems With Quantization and Packet Loss

Yan

Wang

et al. 2020

IEEE Access

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In this paper, the problem of designing the quantized feedback controller for a class of continuous-time switched systems with packet loss and event-driven scheme is considered. Two novel eventdriven schemes are proposed to reduce the amount of data transmission on the network while ensuring the system stability. Under the assumption of dwell time and maximum consecutive packet loss, we obtain the upper bound of Lyapunov function for both mode-match and mode-mismatch situations. By combining with the mode mismatch interval and the upper bound of Lyapunov function, the practical stability of the closed-loop system is guaranteed. Two numerical examples are given to show the potential of the proposed techniques.

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“…On the other hand, in many engineering systems, it is difficult to measure or estimate all transition rates. To reduce the gap between theory and practical applications, some results with incomplete transition rates were stated in other works …”

Section: Introductionmentioning

confidence: 99%

“…To reduce the gap between theory and practical applications, some results with incomplete transition rates were stated in other works. [14][15][16][17] There exist many situations where the state variables of systems are usually unavailable and therefore cannot be used to stabilize the closed-loop systems. 18 Because the observer can estimate the unmeasured states of the system effectively, it may be used to design a controller (called observer-based controller).…”

Section: Introductionmentioning

confidence: 99%

Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Shu

Huang

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper addresses the observer‐based H∞ control of Markovian jump systems with interval time‐varying delays and incomplete transition rates. To reduce the conservatism of proposed results, a modified Lyapunov‐Krasovskii functional is constructed, where an improved delay partitioning method is used by partitioning the delay interval into multiple segments with a geometric sequence. Moreover, the Jensen‐based integral inequality and the reciprocally convex technique are used to tackle the time‐varying delays. Some less conservative stochastic stability criteria are derived in the framework of linear matrix inequalities. Then, the observer‐based H∞ controller is designed. Finally, three numerical examples are given to demonstrate the merit and effectiveness of the proposed method.

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Passivity and passification for switching Markovian jump systems with time‐varying delay and generally uncertain transition rates

Cited by 16 publications

References 46 publications

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Event-Driven Control for Switched Systems With Quantization and Packet Loss

Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

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Passivity and passification for switching Markovian jump systems with time‐varying delay and generally uncertain transition rates

Cited by 16 publications

References 46 publications

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Event-Driven Control for Switched Systems With Quantization and Packet Loss

Observer‐based H∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

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Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates