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Finite-time mixed and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

Author

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  • M. Sathishkumar
  • R. Sakthivel
  • O. M. Kwon
  • B. Kaviarasan

Abstract

This paper is concerned with the finite-time mixed H∞ and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixed H∞ and passive performance index is achieved. Moreover, the robust mixed H∞ and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unify H∞ and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique.

Suggested Citation

  • M. Sathishkumar & R. Sakthivel & O. M. Kwon & B. Kaviarasan, 2017. "Finite-time mixed and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(7), pages 1416-1427, May.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:7:p:1416-1427
    DOI: 10.1080/00207721.2016.1261199
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    Cited by:

    1. Sakthivel, R. & Suveetha, V.T. & Nithya, V. & Sakthivel, R., 2021. "Finite-time reliable filtering for Takagi–Sugeno fuzzy semi-Markovian jump systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 403-418.
    2. Nithya, V. & Sakthivel, R. & Sakthivel, R. & Alzahrani, Faris, 2020. "Dissipative-based non-fragile filtering for fuzzy networked control systems with switching communication channels," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. R. Sakthivel & V. Nithya & Yong-Ki Ma & Chao Wang, 2018. "Finite-Time Nonfragile Dissipative Filter Design for Wireless Networked Systems with Sensor Failures," Complexity, Hindawi, vol. 2018, pages 1-13, October.
    4. Xu, Qiyi & Zhang, Yijun & Qi, Wenhai & Xiao, Shunyuan, 2020. "Event-triggered mixed H∞ and passive filtering for discrete-time networked singular Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 368(C).

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