Stability Analysis Of Discrete Time - Delay Systems Based On

It is well known that time delay is frequently encountered in many real systems,it can often destroy instability and even influence on the system performance, therefore, the research of stability problem for the time-delay systems has the important theory significance and the practical application value. Just because there exists time delay in practice such that a lot of difficulties appear in stability analysis of the time-delay systems, thus, the stability problem of the time-delay systems has become the focus of control theory and application. This paper mainly studies two problems: One is the asymptotically stable problem of the discrete-time linear system with constant time-delay, and the other is the asymptotically stable problem of the discrete-time linear system with time-varying delays.Firstly, by introducing a discrete inner product, a set of discrete orthogonal polynomials(DOPs) is obtained by applying the Gram-Schmidt orthogonalization process. From which, we prove a DOPs-based summation inequality containing a nonnegative integer N as a parameter. The larger the parameter N is, the more accurate the DOPs-based summation inequality becomes. Then, the DOPs-based summation inequality is applied to establish stability criterion for a class of linear delayed discrete-time systems. Compared with the LMI-based stability criteria in most of the literature, the stability criteria in this chapter reduce the computational complexity greatly.By constructing an appropriate augmented Lyapunov-Krasovskii functional, a delay-dependent stability criterion in the form of linear matrix inequality is obtained.Methods proposed in literature is improved, that is, the delay interval is divided into small range to deal with Lyapunov-Krasovskii. The stability criterion given to here is less conservative than the existing ones.