Abstract
Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.
Highlights
Over the past decades, the fuzzy logic control has developed into a successful and fruitful branch of automation and control theory due to the fact that the fuzzy models are the appealing and efficient tools in approximating the complex nonlinear dynamical systems
Definitions 3 and 4 are a first attempt to give the concept of finite-time stability and stabilization for polynomial fuzzy systems based on the basic idea in classical paper [24, 25]
Finite-time stability conditions of the continuous-time polynomial fuzzy system (3) with u = 0, which can be checked by the SOSTOOLS [16], have been derived in Theorem 7
Summary
The fuzzy logic control has developed into a successful and fruitful branch of automation and control theory due to the fact that the fuzzy models are the appealing and efficient tools in approximating the complex nonlinear dynamical systems. A new SOS design framework for robust control of polynomial fuzzy systems with uncertainties is presented by the research group of professor Tanaka [17]. During this period, professor Lam and his colleagues make great contributions to relax the stability and stabilization conditions.
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