Robust Stability And Robust H_∞ Control For Uncertain Time-delay Systems

There are a number of time-delay systems, such as nuclear reactors, chemical engi-neering systems, systems with lossless transmission lines, ship stabilization, aircraft stabilization and so on. The existence of time delay in a systems can cause insta-bility or bad performance. This is why the study of dynamical systems with time delays has received considerable attention over the decades. As is well konw, neu-tral system being a special case of time delay systems in the past. Recently, many researchers have paid a lot of attentions on the problem of robust stability and sta-bilization for neutral systems. However, the mathematical model always contains some uncertain element. Therefore, designing a rubust control such that the system responses meet desired properties is an important thing in control system. Now, the robust H∞control problem recieved considerable attention.The main conclusions in this paper are as follows:(1)Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties. The stability condition for a class of uncertain neutral sys-tems with time delay and uncertainties is studied. Choosen the approriate Lyapunov function, used the Leibnitz-Newton formula and employed free weighting matrices, a new stability condition of neutral system with time delay is derived.Finally, the numerical examples show the effectiveness of the paper.(2)The problem of robust H∞control of uncertain neutral systems with state and input delay is investigated. By using Lyapunov method and Linera matrix inequality (LMI)technology, a new stabilization condition of neutral system with time delay and uncertainties and the robust H∞state feedbace control are derived. Numerical examples are given to illustrate the usefullness of the results.