State Feedback Controller Design for General Polynomial-Fuzzy-Model-Based Systems with Time-Varying Delay

This paper mainly investigates the state feedback controller design and the stability analysis for the general polynomial-fuzzy-model-based systems with time-varying delay. A Lyapunov-Krasovskii (L-K) function with the delay information in integral parts is used in the stability analysis process, and the time-delay terms are solved by an introduced lemma. Here, the assumption that the input matrices and the delay matrices have zero rows at the same time is not needed. A novel square of sum (SOS) optimization method successfully solves the non-convex problem by transforming the nonlinear terms and the time-varying delay matrix items into indices, which are optimized to zero by a semi-definite programming. The resultant SOS conditions are delay dependent, and more flexible stability conditions are obtained by introducing the slack matrices. Numerical simulation proves the effectiveness of the method.