Exponential Stabilization of Markov Jump Systems with Mode-Dependent Mixed Time-Varying Delays and Unknown Transition Rates

Cui, Kaiyan; Zhu, Jianfeng; Li, Chenlong

doi:10.1007/s00034-019-01085-2

Cited by 12 publications

(8 citation statements)

References 37 publications

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“…e 2βθξ T (θ )Rξ (θ) dθ ds and the corresponding result can be validly derived through Theorem 3.1. It should be noted that similar results can be found in Cui et al (2019).…”

Section: Resultssupporting

confidence: 86%

“…Besides, the presented Lyapunov functionalsV ι (t, ξ(t), r(t), σ (t)) (ι = 2, 3, 4) in Theorem 3.1 contain much more information such as the mode-dependent delays, the delayed states and their derivatives. In the view of these points, the resulting derived delay-dependent/mode-dependent stability criterion is expected to be less conservative than that in Cui et al (2019).…”

Section: Resultsmentioning

confidence: 99%

“…Remark 3.1: It is noteworthy that the time-varying delay τ r(t),σ (t) (t) discussed here is mode-dependent, and we also release the constraint condition on the derivative of the time-varying delay, wherein Cui et al (2019) it is required to be strictly less than 1. Besides, the presented Lyapunov functionalsV ι (t, ξ(t), r(t), σ (t)) (ι = 2, 3, 4) in Theorem 3.1 contain much more information such as the mode-dependent delays, the delayed states and their derivatives.…”

Section: Resultsmentioning

confidence: 99%

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Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

Liang

Gong

2020

Systems Science & Control Engineering

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This paper is devoted to the problems of exponential stability and stabilization for piece wise-homogeneous Markovian switching complex-valued neural networks with incomplete transition rates (TRs). Both the time-varying delays and the coefficient matrices are switched among finite modes governed by a piecewise-homogeneous Markov process, where the TRs of the two-level Markov processes are assumed to be time-varying during different intervals. On the basis of an appropriately chosen Lyapunov-Krasovskii functional, some modedependent sufficient conditions are presented to guarantee the unforced network to be exponentially mean-square stable. Then, by proposing certain mode-dependent state feedback controller, stabilization criteria are derived through strict mathematical proofs. At the end of the paper, numerical examples are provided to illustrate the effectiveness of the theoretical results.

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“…e 2βθξ T (θ )Rξ (θ) dθ ds and the corresponding result can be validly derived through Theorem 3.1. It should be noted that similar results can be found in Cui et al (2019).…”

Section: Resultssupporting

confidence: 86%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

Liang

Gong

2020

Systems Science & Control Engineering

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“…In order to ensure that the system can still work normally in the presence of faults and external interference, the fault tolerance and antiinterference ability of the system are very important. Therefore, the stability analysis [1][2][3][4][5], fault detection and filtering [6][7][8][9], fault estimation and fault-tolerant control [10][11][12][13][14] of the system have attracted extensive attention of scholars, and have become a research hotspot in the field of control.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], stochastic MJS with mixed time-varying delays and unknown partial transfer rate are discussed, and their exponential stability in the mean square is analysed. To obtain the less conservative stabilization condition, an appropriate weighting method is proposed in [2].…”

Section: Introductionmentioning

confidence: 99%

Robust fault estimation and fault-tolerant control for nonlinear Markov jump systems with time-delays

Pang

2020

Automatika

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The problem of the robust fault estimation and robust fault-tolerant control, for a class of nonlinear time-delayed Markov jump systems (MJSs) with both actuator and sensor faults, was studied. Firstly, by extending the system state, the actuator fault state vector, the sensor fault state vector and the original system state vector were extended to auxiliary state variables, and the original system was extended to a generalized system. Then, for the singular system, a generalized observer was designed to achieve the simultaneous estimation of its actuator faults, sensor faults and original system state. In addition, based on the observer estimation, a state feedback fault-tolerant controller was designed to make the closed-loop system stable and meet certain performance indicators. By solving linear matrix inequality, sufficient conditions for the existence of generalized observer and fault-tolerant controller were given. Finally, a numerical example and a practical example were given to demonstrate the effectiveness of the proposed approach.

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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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Exponential Stabilization of Markov Jump Systems with Mode-Dependent Mixed Time-Varying Delays and Unknown Transition Rates

Cited by 12 publications

References 37 publications

Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

Robust fault estimation and fault-tolerant control for nonlinear Markov jump systems with time-delays

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

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