Stability And Stabilization For Singular Systems With Time-delay

In many practical fields, it has been found that many problems are modeled by singular systems, such as predator-prey interactions, power systems, population growth models and so on. Singular systems can better describe physical systems than regular ones. On the other hand, time-delay is often countered in various engineering systems, such as chemical, biological, neural and other natural systems, and it is an important source of instability and poor performance. Also, uncertainties inevitably exist in all kinds of physical, industrial and engineering systems because of the simplification of model, change of running environment, and aging of electrical elements and so on. Therefore, the analysis and synthesis for singular systems with time-delay, especially for uncertain singular systems with time-delay are important both in theory and practice.The main contents of this paper are as followed:(1) In chapter 1, the background, the development of the theory and resent research achievements of singular systems are introduced respectively.(2) In chapter 2, the fundamental knowledge of singular systems is introduced. Some definitions, theorems and lemmas which will be used later are presented.(3) In chapter 3, the problem of admissibility for singular systems with multiple time-varying delay is studied. By constructing a new Lyapunov function, first, we develop a delay-dependent sufficient condition, which guarantees that the system is admissible. Then, based on this, a delay-dependent sufficient condition for the existence of a state feedback controller which guarantees that the corresponding closed-loop system is admissible is presented.(4) In chapter 4, for singular systems with bounded fast time-varying state time-delay, by using Lyapunov-krasovskii method and augmented model, a delay-dependent criterion which guarantees that the corresponding closed-loop systems is normal and stable is presented. And for singular systems with bounded fast time-varying state delay and norm-bounded uncertainties, robust PID controller can also be designed.(5) In chapter 5, a conclusion is given. And the perspective on the furthermore study is also proposed.