Delay Independent Criterion for Multiple Time-delay Systems

Based on the fuzzy Lyapunov method, this work addresses the stability conditions for nonlinear systems with multiple time delays to ensure the stability of building structure control systems. The delay independent conditions are derived via the traditional Lyapunov and fuzzy Lyapunov methods for multiple time-delay systems as approximated by the Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined as a fuzzy blending of quadratic Lyapunov functions. A parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic control (FLC) by blending all linear local state feedback controllers in the controller design procedure. Furthermore, the H infinity performance and robustness of the design for modeling errors also need to be considered in the stability conditions.