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Robust stabilization for multi-input polytopic nonlinear systems

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Abstract

This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.

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Authors and Affiliations

  1. College of Computer and Information Engineering, Beijing Technology and Business University, Beijing, 100048, China

    Lipo Mo

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  1. Lipo Mo
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Correspondence to Lipo Mo.

Additional information

This research is supported by the Innovation Project for the Development of Science and Technology (IHLB) under Grant No. 201098.

This paper was recommended for publication by Editor Dexing FENG.

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Mo, L. Robust stabilization for multi-input polytopic nonlinear systems. J Syst Sci Complex 24, 93–104 (2011). https://doi.org/10.1007/s11424-011-8243-9

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  • DOI: https://doi.org/10.1007/s11424-011-8243-9

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