Robust Stability Analysis Of Linear Uncertain Time-delay Singular Systems

Singular systems have more extensive application than normal systems. Time-delay, which is widespread in the practical control systems, and it is an important reason to cause instability and poor performance of the system. The most important feature of the system is the stability. So the research of delay-dependent stability for singular systems with interval time-varying delays has important significance.In this thesis, we study the problem of delay-dependent robust stability for uncertain singular systems. Based on Lyapunov stability theory, we obtain a new delay-dependent stability criterion in terms of linear matrix inequalities (LMI) by selecting appropriate augmented Lyapunov-Krasovskii functional and using Schur complement theorem, integral inequality and reciprocally convex method. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods. The main contents of this thesis are as follows:1. The problem of delay-dependent stability for singular systems with interval time-varying delays is studied. By using a new type of augmented Lyapunov-Krasovskii functional, combined with integral inequality and reciprocally convex method, the delay-dependent stability criterion for testing the stability of singular systems is given in terms of LMIs. Numerical examples are given to demonstrate the improvement of the upper bounds of interval time-varying delay and the effectiveness of the present results.2. The problem of robust stability for time-delay singular systems with norm-bounded uncertainty is studied. By using the Schur complement theorem and the technique for removing uncertainties, the robust stability criterion for the uncertain singular system is given in terms of LMIs. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed methods.