Stability Analysis And Stabilization For The Discrete Systems With Time-Delay

The stability analysis and stabilization problems are put forward for the discrete systems with multiple time-delays by using the comparison principle and frequency domain method of the discrete systems with time-delay.When the coefficients of the systems change in a context of interval, it is an important problem with theory and practice significance to study the delay-independent stability of the multiple time-delay discrete systems with interval coefficient. In the chapter two, the delay-independent stability of the multiple time-delay linear discrete systems with interval coefficient and the multiple time-delay non-linear discrete systems with interval coefficient are studied by using the comparison principle and frequency domain method of the discrete systems with time-delay , and sufficient criterions that the asymptotical stability of the multiple time-delay linear and non-linear discrete systems with interval coefficient are implied by the asymptotical stability of the model gathering time-unvarying ancillary discrete systems are obtained. In some references, the robust stability of no time-delay discrete systems with interval coefficient and single time-delay discrete systems with interval coefficient are studied. Because practice systems have time-delay and sometimes the time-delay is not a single one, so compared with the references, the study of the delay-independent stability of the multiple time-delay discrete systems with interval coefficient has practice application value.The probability of complete control and complete observation of a system is nearly one. With the small fluctuation of a parameter, the incompletely controllable and incompletely observable system can become completely controllable and completely observable system. So when the stability of the ancillary systems is supposed, the stabilization of the neutral type discrete control systems with multiple time-delay and the neutral type interval coefficient discrete control systems with multiple time-delay are studied. In the chapter three, by using the comparison principle and frequency domain method of the discrete systems with time-delay, combining Rouche Theorem, sufficient criterions for the stabilization of the neutral type discrete control systems with multiple time-delay and the neutral type interval coefficient discrete control systems with multiple time-delay are obtained by choosing appropriate feedback controller.