An observer-based robust H∞ controller design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation

This paper deals with the observer-based robust H∞ controller design for the Takagi–Sugeno (T-S) continuous fuzzy systems with uncertainties and external disturbances in the case where the premise variables are not measurable. The main objective of this work is to provide robust stability conditions in terms of relaxed LMIs (Linear Matrix Inequalities) for uncertain and disturbed T-S fuzzy systems with unmeasurable premise variables. Using some matrix transformations and lemmas, sufficient conditions of robust stabilisation are derived in the form of a set of relaxed LMIs guaranteeing an optimal value of the H∞ performance level. The proposed LMI constraints are solved using particle swarm optimisation (PSO) algorithm to obtain the robust controller and observer gains. The proposed method has the advantage of having less predefined parameters against the available methods in the literature. The obtained H∞ control scheme ensures asymptotic stability of the closed-loop system as well as strong disturbance attenuation based on the quadratic Lyapunov function, a fuzzy observer and a fuzzy controller. Two simulation examples are provided to show the effectiveness of the proposed approach.