Study On Stability And Stabilization Of Uncertain Neutral Systems With Distributed Time Delay

Time delays are frequently encountered in the behavior of many practical physical processes, and very often the existence of time delays may result in instability, oscillation or poor performance of a system. In view of that the stability is the basic demand of a dynamical system, the study of the system stability is an important issue in the dynamical system theory. The stability and control issues for delay differential systems have received much interest for recent years, while the development of neutral systems is relatively slow. Neutral delay system contains delays both in its states and in the derivatives of its states. It has a more general form and finds application in such places as population ecology, heat exchangers, electric networks, etc. Moreover, many delay systems can be investigated by transforming to neutral delay systems. The study of neutral delay systems became a hotspot for the last decades. It has profound theory significance and practical value to investigate the stability analysis and synthesis problem of the time delay systems of neutral type.In practical systems, the factors including measure error, change of input condition, abnormal work of sensor and actuator and external disturbance will always bring about the appearance of uncertainties. This paper studies the robust stability, robust H∞control and guaranteed cost control of a class of uncertain neutral delay systems with distributed delay. Using the Lyapunov stability theory combined with the linear matrix inequality and matrix analysis, the delay dependent stability criterion, robust H∞controller and guaranteed cost controller are presented. The main works as follows:1. The robust stability problem for a class of uncertain neutral systems with distributed time delay is studied. An asymptotic stability criterion is established by using the relation between system states, information contained in the model and free weighting matrices.2. The robust H∞control problem for a class of uncertain neutral systems with distributed time delay is discussed. The robust stabilization condition is established by using a descriptor system and LMI approaches and a memoryless state feedback robust H∞controller is designed.3. The guaranteed cost control problem for a class of uncertain neutral systems with distributed time delay is investigated. The guaranteed cost stabilization condition is established by using LMI approach and a memoryless state feedback guaranteed cost controller is designed.