Stability Analysis And Stabilization Of Uncertain Time-delay Systems

The delay phenomenon is prevalent in the industrial and engineering problems. The existence of time-delay makes it more complex to analyze and synthesize of such system. Meanwhile, delay is frequently a source of instability and performance degradation in many dynamic systems. In addition, in the research of real control systems, there exist the uncertainties between the mathematic model and controlled plant, which reflects the existing of model reduction, changes in the environment, the aging of components. Time-delay systems have been an enduring theme for several decades. A great number of monographs have been devoted to this field.The stability analysis and stabilization of time-delay system is the subject of this thesis. Based on linear matrix inequality and numerical methods, the stability and stabilization problems of time-delay systems are studied in this paper. The main contents and novelty are outlined as follows:1. For the linear discrete time-delay systems, the stability and stabilization problems are studied. Based on nonsingular state transformation, sufficient conditions of stability and stabilization are derived, in terms of linear matrix inequality. Then the conditions are improved in the linear interval discrete time-delay systems. Sufficient conditions of D-stability and D-stabilization are proposed for the interval systems. D -stabilization criterion guarantees all poles of the resulting closed-loop system to be placed in a specified circular region. The robust D -stabilizing controller designing method is also proposed. Numerical example shows the feasibility of the proposed method.2. A new stability and stabilization criteria for a class of neutral systems with interval delays are proposed. Based on the Lyapunov functional method, neutral-delay-independent and neutral-delay-dependent robust stability conditions are derived in terms of linear matrix inequalities. Some free weighting matrices are introduced to reduce the conservatism, avoiding any form of inequality restriction. The stabilization conditions are also obtained based on some assumption. Numerical examples are given to show the effectiveness of the proposed criteria finally.3. The stability and stabilizing problem of time-delay systems are studied by the frequency domain stability theory. Based on the numerical methods, we solve the asymptotical stability,α-stability, D -stability problems and robust stability problems of retarded and neutral time-delay systems. Furthermore, based on the numerical methods, the stabilization problem for linear time-delay systems is studied. Finally, numerical examples demonstrate the effectiveness and improvement of our methods.