Input-to-state Stability And Passivity Of Large Delay Systems

The delay phenomenon exists widely in practical engineering, such as power systems, communication systems and networked control systems. In some practical engineering, time-delays may have the following characteristics:the delay bound is less than a fixed value during the most of the time periods, and the stability of the system still can be guaranteed in the role of the delay, and such a kind of delays is referred to as small delay; but in other time period, delay bound may be larger than the fixed constant, and this may lead to the deterioration of the system performance or even make the system unstable, and this kind of delays is called large delays. Systems with this kind of delays are called large delay systems. For example, the continuous packet drop occurs in the Networked Control Systems, occasional failure of the controller or actuator in controller failure research, all may lead to the occurrence of the local large delay. In this case, the traditional method of stability analysis of the delay systems will not be applicable to this class of large delay systems any longer. Therefore, researching of large delay systems will be very important from both theoretical and practical sense.The thesis discusses the Input-to-State Stability (ISS) and passivity of the large delay systems based on switching techniques and Lyapunov stability theory. The concepts of the frequency of large delay period (LDP) and the length rate of LDP are introduced. By making certain restrictions on the frequency and the length rate of LDP, based on a novel piecewise Lypunov functional, the ISS conditions for the nonlinear delay systems with LDP are developed via the form of nonlinear matrix inequalities (NLMIs). Meanwhile, the passivity conditions for delay systems with LDP are also proposed in the form of linear matrix inequalities (LMIs). Numerical examples are given respectively to illustrate the effectiveness of the proposed methods.