Stability Analysis Of A Class Of Uncertain Singular Delay Systems

Singular time-delay system is a very important system. To define strictly, many exist-ing systems are singular and with time-delay. Because of its complexity characteristics, the study of such systems is difficult. But the research clearly has more practical significance. In recent decades, a lot of control theory scholars committed to the study of such systems. For time-delay systems, time delay is often a direct result of the instability. So the stability of time-delay systems has always been a hot research. In this paper, the stability of a class of singular time-delay systems is to be analyzed. The main content is as follows:Firstly, we have summarize the stability analysis of linear matrix inequalities and Lyapunov stability theory. Referencing to the existing literature,we given the sufficient conditions of a system if it is regular,with pulse mode and asymptotic stability.Secondly, study the stability of a class of singular time-delay systems with uncertain-ties. Segmenting the delay and using the Lyapunov theory,we give the sufficient conditions in the form of linear matrix inequalities (LMIs) for the system. We verify that singular time-delay system has less conservatives when its delay was cut apart.Finally, study a class of singular time-delay systems and analyse its H∞performance.