Robust quadratic stability of interval dynamical system with multiply time-delays

Many systems are interval dynamical systems (IDS) with multiply time-delays, such as chemical processes and flight systems. In fact, most researches on stability analysis for IDS with time-delays are quite conservative. To improve the existing results, new methods of analyzing the robust quadratic stability of IDS with multiply time-delays are proposed. First, the convention form of IDS with multiply time-delays is transformed into a certain structured form, which is equal to the former and can be analyzed conveniently. Then, a delay-independent criterion is developed for IDS with multiply time invariant delays. By solving a Riccati inequality, a sufficient condition based on Lyapunov stability theory for quadratic stability of the system was obtained. Finally, the proposed methods are extended to apply to IDS with multiply time varying delays.