Abstract
This paper is concerned with the optimal guaranteed cost sliding-mode control problem for interval type-2 (IT2) Takagi–Sugeno fuzzy systems with time-varying delays and exogenous disturbances. In the presence of the uncertain parameters hidden in membership functions, an adaptive method is presented to handle the time-varying weight coefficients reflecting the change of the uncertain parameters. A new integral sliding surface is presented based on the system output. By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system. Optimal conditions of an $\mathcal {H}_{2}$ guaranteed cost function and an $\mathcal {H}_{\infty }$ performance index are established for the resulting time-delay control system. Finally, an inverted pendulum system represented by the IT2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme.
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