Stability Analysis And Controller Design Of Discrete Time Delay Systems

In real life, time delay can be found everywhere while the existence of time delay usuallyworsens the stability of control systems or even leads to instability and further influences othersystem performances. Besides, time delay often makes it difficult for analysis and synthesis ofcontrol systems. Thus conducting research on systems with time delay is of both great theoreticalsignificance and obvious realistic importance. On the other hand, along with the rapidlydevelopment of modern computer technology, application scope of discrete system, in which timedelay is a common thing, is becoming broader and broader. Therefore the study of discrete timedelay system has gradually been a research hotspot in control field.Research on discrete time delay systems usually contains stability analysis and synthesisproblems. Controller design is most frequently seen referring to synthesis of control systems. Bydesigning controllers appropriately we can overcome some unstable factors in the studied controlsystem. This paper is conducting research based on the above factors.First, the history and present condition of discrete time delay systems are summarized, and somecommonly used analysis methods, whose advantages and disadvantages are analyzed, are summedup. For the past decades, as a mature theoretical approach, Lyapunov functional method has been amost extensively used one in dealing with time delay systems. A great number of researchers andscholars have been focusing on how to handle the cross term obtained from the derivation of theconstructed Lyapunov functionals so as to achieve less conservative results.In chapter three, based on the gained results, an improved LMI-based delay dependent stabilitycriterion on linear discrete system with interval-like time-varying delay is proposed in this paper.By appropriately constructing some Lyapunov-Krasovskii functionals, combined with the properinequality bounding method, some conservativeness have been effectively reduced. The proposedmethod is obtained using no model transformation but using the improved integral inequality andthrough appropriate processing of integral terms with information of delay. It’s worth mentioningthat throughout the proof of the criterion no free weighting matrix variable is added, so the obtainedresult is relatively simple and effective.The fourth chapter studies discrete systems with norm bounded parameter uncertainties andconvex polytopic parameter uncertainties respectively on the basis of the stability analysis inchapter three. And another two improved stability criteria are obtained for the mentioned twopractical systems. Simulation results are used to illustrate the effectiveness and compare differencesbetween the two forms of uncertainties. The fifth chapter deals with the controller design problem according to results of previouschapters. A memoryless feedback controller is designed and a sufficient condition on the existenceof a controller is gained. In order to get the controller gain, this chapter respectively uses conecomplementarity linearization(CCL) algorithm and another iterative algorithm based on linearmatrix inequalities. Corresponding simulations are utilized to verify the effectiveness of thecontroller design and compare effects of two different algorithms.At the end of the paper a conclusion of what have been done in this paper is drawn. Furtherimprovements and research are put forward as well.