Robust [formula omitted] control for uncertain T–S fuzzy systems with state and input time delays: A time-varying matrix-dependent zero-equality method

Abstract

This paper studies robust H∞ control problems for uncertain T–S fuzzy systems with state and input time delay. A modified Lyapunov–Krasovskii functional is constructed by considering membership-function-dependent matrices and delay-product-type matrices. To ensure that the derived results do not involve higher-order delay terms, a method of introducing augmented variables is used. In particular, a time-varying matrix-dependent method is used to link the zero-equalities generated during the mathematical derivation, which increases the freedom of selection of the constant connection matrix and may produce new time-delay cross-term information. Then, a less conservatism stability condition is established, and a robust H∞ controller is designed to ensure that the T–S fuzzy system achieves a predefined H∞ performance level. Finally, two examples are used to verify the feasibility and superiority of the obtained results.