Stability And Stabilization Analysis Of Continuous Linear Systems With Proportional Time Delay

The paper consists of three parts: stability analysis of continuous linear systems with proportional time delay and general continuous linear systems with proportional time delay, stabilization analysis of continuous linear systems with proportional time delay and generalized continuous linear systems with proportional time delay, the robust stability analysis and robust controller design of continuous linear systems with proportional time delay.On the stability and stabilization analysis of continuous linear systems with proportional time delay and general continuous linear systems with proportional time delay, two main works are as follows:(1) A new Lyapunov function is constructed. Using Lyaponov method, some sufficient conditions is proposed for the asymptotic stability of continuous linear systems with proportional time delay. Moreover, the theories are generalized and some criteria of stability are given for general continuous linear systems with proportional time delay.(2) Based on the given sufficient conditions of stability, the stabilization of continuous linear proportional time delay systems is discussed. Especially, a sufficient condition for stabilization of linear system with control delay is given.On the robust stability analysis and controller design of continuous linear proportional time delay systems, the main works in this paper are as follows:(1) The robust stability analysis and discussion for continuous linear proportional time delay systems are carried through. By utilizing the Lyapunov method, combining Riccati inequality, the sufficient conditions of robust stability are given under the condition of highly structured uncertainty and matrix topology structured uncertainty.(2) The problem that robust controller design for systems with control delay and uncertainty is discussed. The sufficient conditions of robust stability by the state feedback are given by utilizing the Lyapunov method.