Abstract
AbstractThe paper focuses on the problem of mixed and passivity guaranteed cost control of an interval‐valued type‐2 (IT‐2) fuzzy system with time‐varying input delay and exogenous disturbance. For this, an IT‐2 fuzzy‐model‐based system with a mismatched membership grade function is formulated. The main objective is to design a proportional‐integral controller that stimulates our system to attain its equilibrium state even with the occupancy of exogenous disturbance and input delay in the system. In addition, a quadratic cost function is constructed such that the cost function of the closed‐loop IT‐2 fuzzy system is lower than the upper‐bound cost index. Mixed and passivity performance indices are then calculated to address the exogenous disturbance in the system. A set of new criteria ensuring the asymptotic stability of the closed‐loop IT‐2 fuzzy system with input delay are derived in terms of linear matrix inequalities with the aid of Lyapunov stability theory and the employment of a Wirtinger‐based inequality. Finally, two example simulations are conducted to validate our theoretical results.
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