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access icon free Control design for interval type-2 polynomial fuzzy-model-based systems with time-varying delay

© The Institution of Engineering and Technology
Received 10/11/2016, Accepted 24/05/2017, Revised 13/04/2017, Published 26/05/2017

In this study, the problems of stabilisation for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, the authors formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

Inspec keywords: fuzzy control; time-varying systems; piecewise linear techniques; fuzzy systems; control system synthesis; approximation theory; asymptotic stability; state feedback; delays; closed loop systems

Other keywords: asymptotic stability; piecewise linear membership function approximations; closed-loop control system; time-varying delay; parameter uncertainties; interval type-2 polynomial fuzzy-model-based system stability; state-feedback interval type-2 polynomial fuzzy controller design

Subjects: Fuzzy control; Stability in control theory; Control system analysis and synthesis methods; Interpolation and function approximation (numerical analysis); Time-varying control systems; Distributed parameter control systems

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