H∞ Guaranteed Cost Fuzzy Control for Non-linear Systems: An LMIs Approach

Mourad KCHAOU, Mansour SOUISSI, Ahmed TOUMI

Abstract

In this paper a state feedback controller is designed to stabilize a discrete-time nonlinear and uncertain system. The Takagi Sugeno (TS) fuzzy model with norm-bounded uncertainties is considered for modelling the nonlinear system. Beyond stability, a mixed (LQ/H) index is also considered, which simultaneously guarantees an upper bound of LQ cost and is robust for unknown external disturbance in the sense of induced H∞ norm. Sufficient conditions for existence of fuzzy state feedback controller are derived in terms of linear matrix inequalities. Finally the effectiveness of the proposed controller design methodology is illustrated through numerical simulations.

Keywords

Fuzzy control, uncertain non linear system, guaranteed cost, robust stability, linear matrix inequalities

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