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Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach

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Abstract

This paper studies the dissipative control problem for two-dimensional (2-D) switched discrete-time linear system represented by Fornasini–Marchesini local state-space (FMLSS) model via dwell-time-dependent Lyapunov function (DTDLF) approach. Consider the definition of (Q, S, R)-\(\alpha \)-dissipativity for 2-D switched discrete FMLSS model in triangular region and based on the DTDLF approach, we first give the linear matrix inequality (LMI)-based sufficient condition on asymptotic stability for the 2-D switched discrete FMLSS model and then propose the LMI-based sufficient condition which can guarantee the given 2-D switched system to be asymptotically stable and strictly (Q, S, R)-\(\alpha \)-dissipative. Furthermore, the dwell-time-dependent dissipative state-feedback controller is designed, and the LMI-based sufficient condition for designing such controller is proposed. Besides, dwell-time-dependent passive state-feedback controller and dwell-time-dependent \(H_\infty \) state-feedback controller could be derived as the special cases of dissipative control from the established result. Finally, illustrative examples are depicted to verify the efficiency and superiority of the proposed techniques.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Grant Numbers: 61603188 and 61972203) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant Number: KYCX19_0252).

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Dingli Hua & Weiqun Wang

  2. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Weiren Yu

  3. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Juan Yao

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  1. Dingli Hua
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  2. Weiqun Wang
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  4. Juan Yao
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Correspondence to Weiqun Wang.

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Hua, D., Wang, W., Yu, W. et al. Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach. Circuits Syst Signal Process 39, 5475–5500 (2020). https://doi.org/10.1007/s00034-020-01440-8

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  • DOI: https://doi.org/10.1007/s00034-020-01440-8

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