LMI-Based Stability Research For Time-Delay Systems

There generally exist time-delay phenomena in real systems. However, systems stability can be destroyed, even systems performance may be influenced due to time-delay. So the study of time-delay systems stability is always a topic of general interest. As to study of delay systems stability , most of contributions are based on Lyapunov stability theory , and all of them are conservative, and furthermore, the processes of reasoning are very complex. But on the other hand, those results are relative to continuous-time delay system.. But with development of digital technique, the role of discrete-time delay system become more and more important. So how to get less conservative results about stability of continuous & discrete time-delay system, attracts considerable attention in the control domain.First, the stability for continuous and discrete time-delay systems is considered respectively. Both delay-independent and delay-dependent stability conditions are established. Based on Lyapunov stability thoery , the delay-dependent , LMI-based and less conservative sufficient conditions for stability of continuous & discrete time-delay systems are obtained respectively. Also the delay-dependent , LMI-based and less conservative sufficient condition for stability of discrete time-delay systems is given.Next,the stability for uncertain continuous and discrete time-delay systems is studied respectively. Based on Lyapunov functional method, the delay-independent, LMI-based and less conservative sufficient conditions for stability of uncertain continuous and discrete time-delay systems are presented respectively via LMI technology. In addition, the delay-dependent, LMI-based and less conservative sufficient conditions for stability of uncertain discrete time-delay systems are provided.Finally, all stability conditions for simple-time delay system are generalized to multiple-time delay system. And a set of analysisapproaches for stability of time-delay system are provided.These conclusions and analysis methods are important to the study for stability of time-delay system. Moreover, the results of numerical examples show that the methods given in this paper are effective.