The Stability Of Uncertain Nonlinear Systems With Time Delay

As a popular topic, robust stability and BIBO stability for uncertain systems with time delay have been widely studied in various engineering, biological, economical, electronic and dynamical systems, nerve network and so on. Recently, many researchers have paid a lot of attentions on the problem of robust stability and BIBO stability for uncertain nonlinear systems with time delay.In this thesis, we concern the stability analysis of uncertain nonlinear systems with time delay. Many criterions for sufficient conditions of the robust stabilization and BIBO stabilization for the uncertain nonlinear systems are obtained by means of Lyapunov function and the method of inequality analysis.The main results are as follows:1. Through Lyapunov function and a solvable algebraic Riccati equation, we obtain the criterion of robust stability (exponential stability) for uncertain nonlinear systems with time delay2. Applying some inequality analysis, we obtain other criterion of robust stability (exponential stability) for uncertain nonlinear systems with time delay.3. Through Lyapunov function and a solvable algebraic Riccati equation, we obtain the criterion of BIBO stability for uncertain nonlinear systems with time delay.4. Using Lyapunov function and linear matrix inequality (LMI), we obtain the other criterion of BIBO stability for uncertain nonlinear systems with time delay.