Asynchronous Dissipative Control for Nonlinear Generalized Markov Jump Systems

doi:10.12068/j.issn.1005-3026.2021.09.002

Abstract

Abstract: The problem of strictly asynchronous dissipative control for a class of continuous time nonlinear generalized Markov jump systems under Takagi-Sugeno fuzzy rules is studied. Firstly， by constructing a less conservative mode independent Lyapunov function， the sufficient conditions for stochastic stability and strict dissipation of generalized system are discussed. Then， the hidden Markov model that is widely used in practice is introduced. By combining the state transition probability with the conditional probability of the hidden Markov process， and through Schur transformation， a fuzzy state feedback controller is designed， which can operate asynchronously with the original system， so as to ensure the stochastic stability and strict dissipation of the closed-loop system. Finally， numerical simulation using Matlab linear matrix inequality(LMI) toolbox is applied to verify the effectiveness of the conclusion.

Key words: asynchronous control; fuzzy rules; generalized Markov jump systems; strict dissipative; stochastic stability

CLC Number:

TP13

YANG Dong-mei， LI Da. Asynchronous Dissipative Control for Nonlinear Generalized Markov Jump Systems[J]. Journal of Northeastern University(Natural Science), 2021, 42(9): 1226-1230.

References

[1]Shen Y，Wu Z G，Shi P，et al.Asynchronous filtering for Markov jump neural networks with quantized outputs［J］.IEEE Transactions on Systems，Man，and Cybernetics Systems，2019，49(6):433-443.
[2]Xia Y Q，Boukas E K，Shi P，et al.Stability and stabilization of continuous-time singular hybrid systems［J］.IEEE Transactions on Automatic Control，2009，45(6):1504-1509.
[3]Li X，Nan J.Strictly dissipative control for Markovian jump descriptor systems［C］//Proceedings of the 35th China Control Conference.Chengdu，2016:1804-1807.
[4]Kwon N K，Park S I，Park P，et al.Dynamic output-feedback control for singular Markovian jump system:LMI approach［J］.IEEE Transactions on Automatic Control，2017，62(10):5396-5400.
[5]Choi H D，Ahn C K，Shi P，et al.Dynamic output-feedback dissipative control for T-S fuzzy systems with time-varying input delay and output constraints［J］.IEEE Transactions on Fuzzy Systems，2017，25(3):511-526.
[6]Dong S L，Wu Z G，Su H Y，et al.Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity［J］.IEEE Transactions on Automatic Control，2019，64(3):1250-1256.
[7]Dong S L，Fang M，Chen S M.Extended dissipativity asynchronous static output feedback control of Markov jump systems［J］.Information Sciences，2020，50(6):275-287.
[8]Wu Z G，Shi P，Shu Z，et al.Passivity-based asynchronous control for Markov jump systems［J］.IEEE Transactions on Automatic Control，2017，62(4):2020-2025.
[9]Sakthivel R，Selvi S，Mathiyalagan K，et al.Reliable mixed H-infinity and passivity-based control for fuzzy Markovian switching systems with probabilistic time delays and actuator failures［J］.IEEE Transactions on Cybernetics，2015，45(12):2720-2731.
[10]Xing S Y，Deng F Q，Qiao L.Dissipative analysis and control for nonlinear stochastic singular systems［J］.IEEE Access，2018，6(3):43070-43078.

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