A Study On D-Stability And D-Stabilization For Linear Uncertain Systems

In engineering application systems, it is usually impossible to describe a practical system exactly. That is because: first, parameter or parasitic processes are not completely known, and some control systems are required to operate within a wide range of different operating conditions. Second, some artificial simplification, for example, there are model reduction, linear approximation and the ignoring of the dynamics which are difficulty for modeling. Usually, these differences can be described as the uncertainties in the model arguments and the uncertainties are measurable and can be restricted in some range. So it is of important theoretical and practical engineering meaning to synthetically study the systems with uncertainties, which now attracts considerable attention in the control theory literature;On the other hand, process delays, which are caused by transmission or on-line analysis, will be a main cause of bad performance or even instability for control systems. Therefore, the research on the time delay systems also attracts considerable attention in the control theory literature. In view of these consideration, D-stability and D-stabilization of linear uncertain systems, including interval systems and uncertain time-delay systems, are studied in this dissertation.Based on Lyapunov stability theory, the D-stability and D-stabilization of linear dynamic interval systems are studied;and then based on frequency-domain stability theory and numerical methods, the D-stability and D-stabilization of linear time-delay systems with norm-bounded uncertainties are studied. The main contents of the dissertation are outlined as follows:1. Sufficient conditions for the quadratic D-stability and quadratic D-stabilization of interval systems are studied. Furthermore, Base on parameter-dependent Lyapunov function methods, sufficient conditions for the robust D-stability and robust D-stabilization of interval systems are studied. Then, a new sufficient conditions which are less conservative for the quadratic and robust D-stability of continuous-time and discrete-time interval systems are given. All results above are represented by LMIs. In the study of robust D-stability and robust D-stabilization, sufficient conditions are based on a parameter-dependent Lyapunov function obtained from thefeasibility of a set of linear matrix inequalities (LMIs) defined at a series of partial-vertex-based interval matrices other than the total-vertex-based interval matrices as in the previous results, which effectively reduces the computation amount. Based on proposed results, an algorithm to analyze the robust D-stability and D-stabilizability of linear dynamic interval systems is given. The robust D-stabilizing controller designing method is also proposed.2. D-stabilization with decay rate and damping ratio restraints for linear time-delay systems with polytopic delays are studied by numerical methods. Futhermore, based on the numerical methods proposed above and matrices measure theory, robust D-stabilization with decay rate and damping ratio restraints for linear time-delay systems with norm-bounded uncertainties are studied. The realization of the method is to place the dominant poles of the system to a specified region which has decay rate and damping ratio restraints through the iteration of the proposed numerical method, which is used to adjust the feedback gain matrix. We illustrate the feasibility of the method by means of simulation examples.The conclusion and further the perspectives are given in the end of thedissertation.