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H ∞ Output Tracking Control for Discrete-Time Switched Systems Based on Switching Method

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Abstract

This paper addresses the H ∞ output tracking control problem for a class of discrete-time switched linear systems. We do not require that the H ∞ output tracking control problem for each individual subsystem to be solvable. Based on the multiple Lyapunov functions approach, a switching law depending on the system state is designed, which, together with the designed controllers, can guarantee that the output tracking error dynamics converges H ∞ asymptotically to zero. In sufficient conditions, we introduce an additional scalar matrix variable to realize the decoupling between the system matrices and Lyapunov matrices. The controller gains can be obtained by solving linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the feasibility of the proposed design method.

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Acknowledgements

This work was supported by the Chinese National Fundamental Research Program under Grant 2009CB320601 and National Natural Science Foundation of China under Grants 61233002 and 61174073.

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Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, P.R. China

    Jiao Li

  2. College of Science, Hebei North University, Hebei, 075000, P.R. China

    Jiao Li

  3. State Key Laboratory of Synthetical Automation for Process Industries, College of Information Science and Engineering, Northeastern University, Shenyang, 110819, P.R. China

    Jun Zhao

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  1. Jiao Li
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  2. Jun Zhao
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Correspondence to Jun Zhao.

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Li, J., Zhao, J. H ∞ Output Tracking Control for Discrete-Time Switched Systems Based on Switching Method. Circuits Syst Signal Process 32, 2487–2502 (2013). https://doi.org/10.1007/s00034-013-9576-5

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