Research On Stability, Regional Stability And Control For Time-Delay Systems

There are time delays in chemical process, metallurgy, aviation, spaceflight, electric power, electronic, economic management and traffic system. So time-delay systems have widely practical backgrounds. Because the existence of time-delay is often the reason of instability and deteriorates the control performance, the studies on time-delay systems stability and control have important theoretical and practical values. On the other hand, there is the corresponding relation between the poles distribution on complex plane and the performance of the traditional control theory. So it has very important theoretical and practical values to study the stability conditions and control law satisfying pole regional distribution for time delaysystems.The research mainly comes from the projects supported by National Natural Science Foundation of China(60074026) and Guangdong Province Science Foundation (000409). The regional stability and control, H_∞ robust control, reliablecontrol for linear time-delay systems, the regional stability and control for linear large-scale time-delay systems by analyzing the distribution of the roots of their transcendental characteristic equations in the new technology, and the delay-dependent stability for two class of important nonlinear time-delay systems by Lyapunov functional technology are studied in this paper. The main researches include:1. Robust regional stability of a class of linear uncertain systems with multiple unknown constant delays is studied. The stability conditions such that all poles of the system under consideration lie in a certain symmetric region in the left-hand side of the complex plane are established. The result is presented in the form of Linear Matrix Inequalities (LMIs) so that it is feasible numerically. Besides, the α - stability and asymmetrical stability are established.2. For a class linear time-delay systems with bounded uncertainties scalar or norm-bounded uncertainties, a robust stabilization condition and the corresponding controller designing method which lets the closed-loop system satisfy the regional stability and H_∞ performance are given. The result is...