Robust Stability Of Uncertain Time Delay Neutral System

In this thesis, we concern the stability analysis of uncertain neutral systems with time delay. Many criterions for sufficient conditions of the robust stabilization for the uncertain neutral systems are obtained by means of Lyapunov function and linear matrix inequality technology. The main results are as follows:1. Based on a descriptor model transformation and constructing Lyapunov function, we consider the stability problem of uncertain neutral system with mixed multiple time-varying delays. The criteria is given in the form of linear matrix inequality(LMI). Numerical examples are given to indicate significant improvements over some existing results.2. The robust stability of uncertain neutral systems with time-varying discrete delay and nonlinear uncertainties are investigated. By using Lyapunov method, some inequality analysis and the method of decomposing the matrices, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab. Comparing with the existed results, ours are less conservative.3. The robust stability of uncertain neutral systems with mixed delays and nonlinear uncertainties are investigated. The Lyapunov method and some inequality analysis are used to obtain some delay-dependent stability criteria.4. The problem of robustly exponentially stability for uncertain neutral systems with discrete delay is studied in this paper. Based on Using the S-procedure, constructing Lyapunov function and applying the descriptor system approach, new delay-dependent robustly exponentially stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robustly exponentially stability of the considered systems. Some examples are given to indicate significant improvements over some existing results.5. The problem of robustly exponentially stability for two uncertain neutral systems with time-varying discrete and distributed delays is studied in this paper. According to adding slack matrices to construct Lyapunov function and using some inequality analysis and the method of decomposing the matrices, new delay-dependent robustly exponentially stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robustly exponentially stability of the considered systems. Comparing with the existed results, ours are less conservative.