Application of fuzzy H{sup}∞ control via T-S fuzzy models for nonlinear time-delay systems

摘要

This paper deals with the problem of stability analysis and stabilization via Takagi-Sugeno (T-S) fuzzy models for nonlinear time-delay systems. First, Takagi-Sugeno (T-S) frizzy models and some stability results are recalled. To design fuzzy controllers, nonlinear time-delay systems are represented by Takagi-Sugeno frizzy models. The concept of parallel-distributed compensation (PDC) is employed to determine structures of frizzy controllers from the T-S frizzy models. LMI-based design problems are defined and employed to find feedback gains of frizzy controller and common positive definite matrices P satisfying stability a delay-dependent stability criterion derived in terms of Lyapunov direct method. Based on the control scheme and this criterion, a frizzy controller is then designed via the technique of PDC to stabilize the nonlinear time-delay system and the H{sup}∞ control performance is achieved in the mean time. Finally, the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.