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

  • Hak-Keung LamEmail author
Chapter
Part of the Studies in Systems, Decision and Control book series (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.

Keywords

Polynomial Fuzzy Model Lyapunov Function Candidate Piecewise Linear Membership Function Premise Membership Functions Stability Analysis Results 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of InformaticsKing’s College LondonLondonUK

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