The Control Problem Of Discrete Time-delay Systems Is Studied

Delayed phenomenon exists widely in many practical systems, and in order toapply the computers as the auxiliary tool to analyze and control the system, thediscretization of continuous-time systems is required by researchers. In addition, thesingular system model can better describe many practical system (including electriccircuit systems, economic systems, etc.). Therefore, investigating the methods toanalysis and control (general) discrete time-delay systems is very signifcant andvaluable. The main contents in this thesis are as follows:For a class of discrete-time systems with an interval time-varying state delay,a appropriate Lypunov function is constructed and delay partitioning technique isused to investigate sufcient conditions under which the class of considered systemscan be stabilized via static output feedback controller. At the same time, it istheoretically proven that the approach proposed in this thesis is superior to theexisting ones. Then, based on the results of static output feedback controller, thestabilization problem via dynamic output feedback controller is also investigated.For a class of discrete singular time-delay LPV systems, based on delay parti-tioning technique, a appropriate Lypunov function with more information of delayis constructed, to investigate a robust and asymptotical stability criterion. It istheoretically proven that the approach proposed in this thesis is superior to oneproposed in [Joint48th IEEE Conf. Decision Control and28th Chinese ControlConf.,2009,7210–7215]. At the same time, a theorem which theoretically proventhat the results are less conservatism with more meticulously delay partitioning isgiven. Then, the stabilization problem via state feedback is also considered.For a class of discrete-time singular systems with interval time-varying delaysin state and input, a appropriate Lypunov function is constructed and the Jenseninequality technique is used to obtain a new bounded real lemma for the correspond-ing unforced system. It is theoretically proven that the approach proposed in this thesis is superior to one in [J. Comp. Appl. Math.,2008,217:194–211], and has thesame conservativeness with one in [J. Franklin Inst.,2010,347:1704–1722]. At thesame time, it is also point out a error in [J. Franklin Inst.,2010,347:1704–1722].Then, based on the obtained bounded real lemma, the considered robust H∞controlproblem is solved.In this thesis, cone complementarity linearization method and scaling the matrixinequality technique are used to deal with the involved nonlinear problems. Thenumerical results of several examples and their simulations illustrate the efectivenessof the approach proposed in this thesis.