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Stability Analysis of Polynomial Fuzzy Model-Based Control Systems Using Fuzzy Polynomial Lyapunov Function

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Polynomial Fuzzy Model-Based Control Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 64))

Abstract

This chapter proposes a fuzzy polynomial Lyapunov function candidate, which consists of a number of local sub-Lyapunov function candidates, for the stability analysis of polynomial fuzzy model-based control systems where the contribution of each local sub-Lyapunov function candidate to the overall fuzzy polynomial Lyapunov function candidate is governed by the membership functions and fuzzy rules. Piecewise linear membership functions are proposed for the implementation of membership functions in the fuzzy polynomial Lyapunov function candidate to alleviate the difficulty in the stability analysis caused by the time derivative of the membership functions. Furthermore, the piecewise linear membership functions divide the overall operating domain into operating sub-domains. A local polynomial fuzzy controller is proposed for the corresponding operating sub-domains. During the control process, the corresponding local polynomial fuzzy controller is employed for the control of the nonlinear plant resulting in switching control strategy. SOS-based stability conditions are obtained to determine the system stability and synthesize the controller. A simulation example is presented to demonstrate how the number of sub-domains influences the capability of finding feasible solutions and show that the proposed SOS-based stability conditions are more relaxed compared with some published ones.

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  1. Department of Informatics, King’s College London, London, UK

    Hak-Keung Lam

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Lam, HK. (2016). Stability Analysis of Polynomial Fuzzy Model-Based Control Systems Using Fuzzy Polynomial Lyapunov Function. In: Polynomial Fuzzy Model-Based Control Systems. Studies in Systems, Decision and Control, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-34094-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-34094-4_10

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  • Online ISBN: 978-3-319-34094-4

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