Analysis Of Stability Of Singular Systems With Delay And Controller Design

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 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.Firstly, the present situation and the existent problems of singular systems with delay are introduced. Secondly, the fundamental knowledge and prepared lemmas are considered. Finally, the main research task is studied:For singular time-delay systems, used method of the Lyapunov second method combined LMI. The new criteria of stability of singular systems with time delay is given. This chapter first gives the stability criterion when the corresponding delay upper bound of the derivative is known. Then, gives the stability criterion delay when time can not guide or the upper bound of the derivative is unknown. The last two inference give out the stability criterion of the corresponding normal system.Based on the stability conditions, give out the situation of the delay upper bound of the derivative are known and unknown, can make the controller design for stability of the closed-loop system with state feedback...