On Stability Analysis And Control Design Of Switched Delay Systems

For many systems important to safety (such as nuclear power station, spacecraft), inaddition to the function of continuous control, there also needs some logical control func-tion of protection or emergency shutdown, to protect industry important to safety during theoperation. On the other side, in practical process of continuous control time delay is not in-evitable in such systems and affects their dynamics. Regarding this kind of logical control asswitching phenomenon, the systems important to safety which influenced by logical controland time delay simultaneously can be modeled as switched delay systems. This disserta-tion considers the switching control problems in systems important to safety and focuses onresearch of switched delay system. Due to the interaction among the continuous dynam-ics and discrete dynamics and time delays, the behavior of such systems may become morecomplicated and the research may have important application and theoretical values.This dissertation starts with the study of time-delay systems. We consider the problemof stability analysis and give some stability results with less conservatism, then study thecontrol design for the system with input delay. Based on the research on time-delay systems,by taking switching phenomenon into account, we also consider the problems of stabilityanalysis and control design for switched delay systems under the time-dependent switchingstrategy. Furthermore, considering the state-dependent switching strategy, we investigatethe problem of switching strategy design which guarantees the stability of switched delaysystem, and then the design problem of both controller and switching strategy. The maininnovations of this dissertation can be summarized as follows.(1) The problems of stability analysis and control design are studied for linear systemswith time-varying delay. Considering different kinds of time-varying delay, based on Lya-punov theory, some new criteria are presented by using integral inequality method to analysisthe asymptotical stability of time-delay systems. For synthesis problem of control systemswith time-varying input delay, a new design method based on state transformation is pro-posed to facilitate controller designing efficiently and the method is also applicable to the existing stability results for controller designing. The examples show that the stability crite-ria give greater upper bound of delay which guarantee the stability of system, and the newdesign method can be applied efficiently for the problem of control design.(2) Consider linear systems with time-varying delay, a novel delay decompositionmethod is presented to investigate the stability problem. Since more information of sys-tem state can be take into full consideration for analysis, the upper bound of the derivativeof the Lyapunov functional is estimated more tightly, which makes stability results less con-servative. By applying integral inequality technology and properly constructing the Lya-punov functional which is dependent on the way of decomposition, some results for delay-dependent stability and control design are given. The numerical examples show that ourstability results of time-delay systems are less conservative than the existing ones and theproposed method for control design is feasible.(3) For linear continuous-time switched systems with time-varying delay, we considerthe problem of switching strategy and control design to guarantee the exponential stabilityof such switched time-delay systems. Under a class of switching signals counting with av-erage dwell time and using multiple Lyapunov functional technique, by constructing properLyapunov functional, the switching design methods are presented to guarantee exponentialstability of such systems with exponential decay estimates, the numerical example gives alower bound of average dwell time than existing results which implies that our result allowsa higher frequency of switching. For control design, we extend the new state transformationtechnology proposed in time-delay systems to the switched time-delay systems, which suc-cessfully solves control design problem. The simulation example illustrates the feasibilityand effectiveness of the proposed method.(4) Considering the state-dependent switching method, it is the first to apply maximumregion function strategy to the research of switched time-delay systems. We partition thestate space into several regions for different subsystems and define the surface at whichswitching occurs, by introducing a new type of energy function for each region to measureoverall abstract energy of the switched systems, we obtain some new delay-dependent resultsfor designing the switching strategy. For the problem of control design, we improve theprevious state transformation technology, which makes the control design more convenient.Examples obtain greater upper bounds of delay which means that our approach is effectivein reducing conservatism, and the improved control method is also feasible even throughconsidering sliding motion.