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Partial Stability and Adaptive Control of Switched Nonlinear Systems

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Abstract

Partial stability and the adaptive control problem are studied for switched nonlinear systems in this paper. A sufficient condition for partial stability of switched systems is presented using multiple Lyapunov functions. Then, for a switched system with uncertain parameters, a design method is proposed to design adaptive controllers for subsystems and a switching law. Asymptotical stability is achieved even though all the subsystems are unstabilizable, which covers the classical adaptive control of non-switched systems as a special case. The proposed theory and method are validated by an example.

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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

    Xia Wang

  2. College of Electronic and Informational Engineering, Hebei University, Hebei, 071002, P.R. China

    Xia Wang

  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. Xia Wang
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Correspondence to Xia Wang.

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Wang, X., Zhao, J. Partial Stability and Adaptive Control of Switched Nonlinear Systems. Circuits Syst Signal Process 32, 1963–1975 (2013). https://doi.org/10.1007/s00034-012-9544-5

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  • DOI: https://doi.org/10.1007/s00034-012-9544-5

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