Study On The Stability And L₂-gain Of Descriptor Systems With Large Delays

The models of many practical problems are described by descriptor systems, which are commonly encountered in many fields such as economic system, power system, industrial control system and flight control system. From the view of theoretical analysis and the engineering practice, many papers have investigated them widely. Meanwhile, time delay is a common phenomenon encountered frequently in vast engineering control. At present, the study for descriptor delay systems has attracted wide attention in the field of international control. During the methods for studying descriptor delay systems, the delay bound is less than a fixed value on the whole time domain, and such a kind of delays are referred to as small delays. However, in practical engineering, for example, the continuous packet drop in the networked control systems, and the occasional failure of controller or actuator in fault-tolerant control, all may lead to the delay bound larger than the fixed constant. This kind of delays is called large delays which may lead to the deterioration of the system performance or even make the system unstable. Therefore, the study for descriptor systems with large delay period is very significant.In this paper, attention is focused on the exponential stability and the L2-gain problems for the descriptor systems with large delay period. The main contents including:1. For the exponentially stable of the descriptor systems with large delay period problem, the descriptor systems can be viewed as switched systems with switching signal depending on the size of delay. Based on the switching method, we give the restriction of frequency and length rate of LDP to study the large delay descriptor systems. By using classical fast and slow subsystems decomposition method, and constructing a novel Lyapunov functional, the sufficient conditions are obtained so that under which the descriptor systems are regular, impulse free and exponentially stable.2. To the L2-gain problem of the descriptor systems with large delay period, the systems can be viewed as switched systems with two subsystems, based on the switching method, the novel Lyapunov-Krasovskii functional method and free weighting matrix technique to guarantee the concerned descriptor systems are regular, impulse free and have weighted L2-gain.