Research On Robust Stabilization And Control For Uncertain Time-delay Descriptor Systems

In control system design process, it is almost impossible to use a mathematical model which is fully reflected the actual controlled object. The complexity of the controlled object makes a gap between the actual object and the model which we have gotten. This gap can be regarded as the uncertainty of system model. On the other hand, delay phenomenon is existed in many practical systems, which will often lead to the instability and poor performance of the dynamic response of the system. descriptor system is often considered as a kind of dynamical systems which is more general than any other system and has been widely applied. Many physical systems are described more convenient and natural by descriptor systems. Recently, a lot of research efforts have been drawn on the study of descriptor systems. Therefore, the analysis and synthesis of uncertain generalized time-delay systems are important both in theory and practice.Using LMI approach and Lyapunov stability theory, the problems for delay-dependent robust stabilization and robust H∞control are researched for uncertain descriptor systems. The main results and contributions are described as follows:1. A class of uncertain descriptor systems with variable delay intervals robust stabilization problem is studied. The confident condition of the nominal system with regular, impulse free and asymptotically stable is given. To the derivative bound φ≥1of time delay d(t) it introduced the adjustable parameters a(0<a<1). In order to get the less conservative conditions it proposed a delay decomposition approach. Meanwhile, a robust stabilization state feedback controller design method of closed-loop system is given. The conclusions are presented in the form of LMI. Using the LMI toolbox in Matlab a numerical example is given to show the effectiveness and reasonability of conclusion.2. H∞control problem for a class descriptor neutral systems with state delay and input delay uncertain robust is discussed. Constructing a new Lyapunov function and using the integral inequality and linear matrix inequality, the asymptotically stable sufficient conditions for the closed-loop system is given. The controller is designed to ensure that the closed-loop system is asymptotically stable and satisfies the given performance index. Finally, using the Matlab LMI Toolbox a numerical example is provided to illustrate the effectiveness of the conclusions.