The Stability And Computation Of Time-delay Systems

Many processes with time delay are often encountered in various systems, such as aviation, spaceflight, electric power, chemical process, metallurgy, economic management and traffic systems. So time-delay systems have widely practical background. Moreover, the existence of time-delay may often results in instability and deteriorates of the performance of systems, the studies on stability and computation of time-delay systems have important theoretical and practical values.This dissertation focuses on the stability of linear delay differential systems and discretization of continuous time-delay systems with time-delay in states.The main results include:In Chapter 1, we study the delay-independent stability of linear neutral systems with commensurate delay. We will given a necessary and sufficient algebraic criterion for delay-independent stability. According to this criterion, to show the asymptotic stability of a neutral system, it suffices to check whether some polynomials are Hurwitz stable and wether a real polynomial with one variable has real roots, which are very easy to be tested. In the last section an illustrative example is given to demonstrate the validity of our new criterion.In Chapter 2, we studies the stability of linear retarded differential systems with two delays. Necessary and sufficient algebraic condition for delay-independent stability is given. According to this criterion, to show the asymptotic stability of this system, it suffices to check whether one polynomial is Hurwitz stable, wether two real polynomials with one variables have real roots and one real polynomial with two variables has real roots. Moreover, we get the algorithm that asserts whether this polynomial with two variables has real roots. An example is given to illustrate the stability criterion.In Chapter 3, we study the discretization of continuous time-delay systems, by using Hermite Approximation of the delay state which cannot be expressed explicitly.