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Relaxed Sum-of-squares Approach to Stabilization of Polynomial Fuzzy Systems

Lizhen Li* and Kazuo Tanaka
International Journal of Control, Automation, and Systems, vol. 19, no. 8, pp.2921-2930, 2021

Abstract : In this paper, a sum-of-squares (SOS) approach is presented to deal with the stabilization of polynomial fuzzy systems. First, we propose a novel non-convex control framework that is equivalent with the basic SOS-based stabilization condition, which is also non-convex. Secondly, by fixing a determinant variable, the novel control framework is converted into convex conditions. The main feature of the proposed approach is that the developed SOS conditions are convex and hence numerically tractable. Moreover, the number of the SOS conditions is equal to that of fuzzy rules, leading to comparatively less computational demand. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

Keyword : Convex condition, polynomial fuzzy system, state feedback control, sum of squares (SOS).

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