A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems

Zhang, Ruimei; Liu, Xinzhi; Zeng, Deqiang; Zhong, Shouming; Shi, Kaibo

doi:10.1016/j.fss.2017.12.010

Cited by 85 publications

(46 citation statements)

References 39 publications

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“…Remark The sawtooth structural LKFs V 4 ( x ( t ), t , σ ( t )) and V 6 ( x ( t ), t , σ ( t )) were respectively proposed by Zhang et al They can take full advantage of the available information on sawtooth structure characteristic. Under the aperiodic sampling ETCS, V 4 ( x ( t ), t , σ ( t )) and V 6 ( x ( t ), t , σ ( t )) are introduced to investigate the stabilization problem of MJS for the first time.…”

Section: Resultsmentioning

confidence: 99%

“…Recently, for stabilizing MJSs, various control strategies have been proposed, such as state feedback control, adaptive control, and sliding mode control . Among them, with the development of digital technology and communication, sampled‐data control has attracted much more attention because of its low cost consumption, reliability, and easy installation . Additionally, in practical implementation, especially under the network environment, computation and communication resources are usually limited.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, the obtained stabilization criteria for MJSs in the work cited above may be conservative because the constructed LKFs are required to be positive definite all the time and most of the available information on the sawtooth structure of time‐varying artificial delay has not been fully adopted. Most recently, it has been demonstrated that the newly proposed input‐delay‐dependent LKF in the work of Zhang et al and Witinger‐inequality‐based time‐dependent LKF in the other work of Zhang et al, which have less constraints and can fully capture the information on sawtooth structure, are very effective in conservatism reducing for sampled‐data systems. Accordingly, how to introduce these two useful LKFs for studying event‐triggered stabilization problem of MJSs to get less conservative result is the third motivation of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…20,21 Among them, with the development of digital technology and communication, sampled-data control has attracted much more attention because of its low cost consumption, reliability, and easy installation. [22][23][24][25][26][27] Additionally, in practical implementation, especially under the network environment, computation and communication resources are usually limited. Therefore, a core problem is to achieve a controller that less transmission burden can be carried.…”

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confidence: 99%

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Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

Xie

Zhang

Zeng

et al. 2020

Intl J Robust & Nonlinear

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Summary This paper investigates the strictly dissipative stabilization problem for multiple‐memory Markov jump systems with network communication protocol. Firstly, for reducing data transmission, we put forward a novel mode‐dependent event‐triggered communication scheme based on aperiodically sampled data. Secondly, a Markov jump system with general transition rates is considered to make the result more applicable, where the transition rates of some jumping modes allow to be completely known, or partially known, or even completely unknown. Thirdly, a less restrictive Lyapunov‐Krasovskii functional, which is only required to be positive definite at end points of each subinterval of the holding intervals, is first introduced for event‐triggered control issue. Based on the above methods, a sufficient condition with less conservatism is obtained to ensure the stochastic stability and dissipativity of the resulting closed‐loop system. Meanwhile, an explicit design method of the desired controller is achieved. Finally, two numerical examples are presented to demonstrate the effectiveness and advantage of the proposed method.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

Xie

Zhang

Zeng

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Whether the above application is successful depends on a key prerequisite that the system has some stability. So stability analysis of various neural networks has become a hot research topic [15][16][17][18][19][20][21][22][23][24][25]. In practical experience, neural networks are often disturbed by environmental noise.…”

Section: Introductionmentioning

confidence: 99%

Boundedness and robust analysis of dynamics of nonlinear diffusion high-order Markovian jump time-delay system

Rao

Zhong

2018

Adv Differ Equ

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In this paper, we prove the existence and uniqueness of the equilibrium solution of the system by using the M-matrix and the topological degree technique and study the boundedness and robustness of dynamics of reaction-diffusion high-order Markovian jump Cohen-Grossberg neural networks (CGNNs) with p-Laplacian diffusion, including the common reaction-diffusion CGNNs. The obtained criteria are applicable to computer Matlab LMI-toolbox, which is suitable for large-scale calculations of actual complex engineering. Finally, a numerical example demonstrates the effectiveness of the proposed method.

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Robust fractional‐order fast terminal sliding mode control with fixed‐time reaching law for high‐performance nanopositioning

Wang

Zhou

et al. 2022

Intl J Robust & Nonlinear

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For high-performance trajectory tracking at the nanometer scales, this paper presents a new fast terminal sliding mode controller, which combines a recursive integer-order non-singular high-order sliding manifold and a fractional-order fast fixed-time reaching law to ensure globally fast convergence, and adopts a time-delay-estimation (TDE) based disturbance estimator deeming the designed controller robust to parameter uncertainty. Stability of the designed controller is verified through the Lyapunov framework, where the full analyses of convergence region and settling time are also presented. The tracking performance is experimentally verified on a piezo-stack driven nano-positioning platform. To showcase the performance improvements, measured closed-loop performance of the proposed controller is contrasted with those obtained using three benchmark control approaches namely the basic Proportional-Integral-Derivative (PID), the popular Positive Position Feedback with Integral action (PPF+I), and the traditional linear sliding mode controller (LSMC).

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A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems

Cited by 85 publications

References 39 publications

Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

Boundedness and robust analysis of dynamics of nonlinear diffusion high-order Markovian jump time-delay system

Robust fractional‐order fast terminal sliding mode control with fixed‐time reaching law for high‐performance nanopositioning

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