The Stability And Sliding Mode Variable Structure Control Of Time-Delay Systems

The time-delay is a kind of physics phenomenon which exists in the natural extensively, the existence of the time-delay makes the stability analysis much more complicated. The research on the stability of systems is an important area in the dynamical systems theory. The stability is not only a basic demand of the dynamical systems, but also a necessary precondition of keeping all systems can be movemented normally. In the last several decades, the research of the neutral type systems with time-delay had became a hotspot in the control area and had attracted more and more researchers. These systems contain not only information of the past state, but also information of the derivative of the past state. These systems can be depicted by the neutral type functional differential equations with time-delay. For the researching on some properties of the neutral systems with time-delay, some necessary theoretical basic and methods will be offered to resolve actual problem for correspond for the people.Sliding mode variable structure control (SMC) is becoming an important branch of modern control theory. Due to SMC have a complete robust for the parameter disturbances, Exterior disturb and uncertainties of the systems, it is extensive concerned by the domestic and international scholar. However, in actual systems, because of switching equipment exist inevitably inertial, so the variable structure control(VSC) systems switch over back and forth between the different control logic, as a result, it causes violent chattering of the actual sliding mode systems, it is taken place impossibly and accurately on the switching plane. The chattering phenomenon has been a main difficult for SMC theory in actual application. How to eliminate the chattering phenomenon while keeping the robustness of SMC is the most important problem to be resolved for SMC in actual application.Discrete-time VSC systems (DVSCs) with time-delay are researched mainly in the paper. Since 1950s, VSC has been increasingly applied into many industrial domains, such as motors and power systems, spacecrafts, robots, chemical engineering and so on. In the present digital era, with the advance of microcomputer technology, the DVSCs research on the sampled systems become a hot-spot. In the DVSCs, the switching control is not continuous and smooth any more, it is only a quasi-sliding mode. This is because of the chattering phenomena which caused by the limited sample frequency and time-delay. On the other hand, because of the inherent property of the performance organization, the signal collect and deliver factors will make many control systems always with time-delays. The existence of time-delay usually makes the stability and the control characteristics of the systems become bad, this makes that at the time of research DVSC we should morely consider the delay factor, so the research on DVSC with time-delay will become meaningful and worthful.The main contents are as follows:1. The historical background of problems and the main works in the paper are introduced.2. The research background and research present condition of problems are introduced for the neutral type systems with time-delay. The stability problem of the neutral systems with time-delay is discussed, and a sufficient condition of the asymptotic stability is obtained for the time-invarying neutral systems with time-delay.3. The development history, research status and the characteristics of VSC are summarized. The related concepts, the existence condition , the arrival condition and some contral methods of sliding mode in DVSCS are given.4. The VSC of discrete-time systems with time-delay are researched, a variable rate reaching law is introduced, a control method based on combinatorial reaching law is given.