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More Relaxed Non-quadratic Stabilization Conditions for TS Fuzzy Control Systems using LMI and GEVP

Navid Vafamand and Mokhtar Sha Sadeghi*
International Journal of Control, Automation, and Systems, vol. 13, no. 4, pp.995-1002, 2015

Abstract : In this paper, a new systematic approach is presented to further decrease the conservativeness in stability analysis condition and controller design. Non-quadratic Lyapunov function is utilized to derive stability conditions in terms of linear matrix inequalities. Also, the control problem is formulated in a generalized eigenvalue problem. Considering the concept of decay rate and control input constraint, a new systematic procedure is proposed to calculate a maximum bound for the upper bounds of the time derivatives of the membership functions. Moreover, some slack matrices are introduced that help to reduce conservativeness. The number of inequalities is few compared to the existing results in literature, which helps the feasibility in the case of large number of fuzzy rules. Simulation examples and comparison results demonstrate the merits of this method.

Keyword : Linear matrix inequality, parallel distributed compensation, relaxed conservativeness, stability conditions, Takagi–Sugeno fuzzy model.

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