Robust Stability and Stabilization Criteria for Systems with Delays

Systems with time delay can be found in many fields. Time delay may affect systems' performance and stability, and tools are needed to detect the stability of systems with time delay. Many tools have been developed in the frequency and the time domains. One of the most powerful tools is the Lyapunov- Krasovskii method which can be applied for general systems and different delay types. A special version of that method has been used by many researchers in the recent years. That version establishes sufficient conditions for the systems' stability, and the recent research in that direction tried to reduce the conservatism of the developed method. In the present work some theorems for different types of delay are developed, which give less conservative results than those previously reported. Moreover, the present methods are extended to design feedback controllers, which ensure robustness against disturbances. All the developed theorems are compared with the recent results, and verified through simulations.