H∞-Based Tracking Control for Nonlinear Systems With A Sampled-Data PI-Type Controller: A Nonuniform Sampled-Time-Dependent Functional

This article investigates the $H_{\infty }$ -based tracking control problem for nonlinear systems through the Takagi-Sugeno (T-S) fuzzy technique. A nonuniform sampled-time-dependent functional (NSTDF) is proposed, which removes the constraints of the conventional looped functional (LF) and relaxes the condition of the functional derivative. Combining the NSTDF with $H_{\infty }$ theory, a novel theorem for $H_{\infty }$ performance analysis of sampled-data systems is given, which loosens the positive-definite constraint on Lyapunov matrices in traditional LFs. By introducing the error integral state, an augmented system is constructed, and a proportional-integral (PI)-type controller that incorporates the external disturbance, transmission delay, and packet dropouts is designed to enable the tracking control. Thus, the $H_{\infty }$ -based tracking control issue is converted into an $H_{\infty }$ -based control problem for the augmented system, and the control conditions are derived via the proposed methods. Finally, the wind energy conversion system (WECS) and Rossler’s system clarify the feasibility and merits of the provided methods.