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Stability Analysis of Polynomial Fuzzy Model-Based Control Systems Using Switching 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 switching 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 switching is dependent on the system states. When the system state vector falls into the pre-defined local operating domain, the corresponding local sub-Lyapunov function candidate is employed to take care of the system stability. Corresponding to each local sub-Lyapunov function candidate, a local polynomial fuzzy controller is employed for the control of the nonlinear plant resulting in a switching polynomial fuzzy control strategy. A favorable form of switching polynomial Lyapunov function candidate is proposed to make sure that smooth transition among the local sub-Lyapunov function candidates takes place at the switching boundary for a valid Lyapunov function candidate. SOS-based stability conditions are obtained to determine the system stability and synthesize the controller. A simulation example is presented to show the effectiveness of using different number of sub-domains and their capability of finding feasible solutions.

Keywords

Polynomial Fuzzy Model Polynomial Switching Lyapunov Function Candidate 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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