State Estimation And Feedback Stabilization For Descriptor Systems

Based on the recent research on the theory of descriptor system and singularly perturbed system, networked control methods and control methods with input satu-ration, this dissertation investigates state estimation and feedback control problems for descriptor systems. The main results in this dissertation are as follows:1. For continuous descriptor systems, a class of parametric generalized alge-braic Riccati equations are proposed and the necessary and sufficient conditions for the existence of the solutions are obtained. In addition, the asymptotical property of the solution with respect to the parameter is given. Base on the asymptotical prop-erty, low-gain state feedback control law is proposed such that the liner descriptor system with input saturation is semi-globally asymptotically stable. Furthermore, a scheduling technique is proposed and global asymptotical stabilization feedback control law is obtained. For linear continuous-time descriptor systems subject to in-put saturation and external disturbance, simultaneous stabilization feedback control laws in both semi-global and global sense are obtained.2. Semi-global output regulation problem for linear descriptor systems with input saturation is investigated. Base on the asymptotical property of the solution of the parametric generalized algebraic Riccati equation, state feedback control law is designed to solve the output regular problem which involves no system transfor-mation.3. Both coder-decoder-estimator and coder-decoder-controller procedures are constructed for linear discrete-time descriptor systems with a limited digital com-munication channel. The sufficient detectable and stabilizable conditions are pro-posed. In addition, when data package lost exists in the communication channel, the sufficient detectable and stabilizable conditions are also proposed.4. A new bounded real lemma is proposed for discrete descriptor systems, which indicates that the admissibility of the descriptor system with a prescribed H∞level is equivalent to the admissibility of an augmented discrete singular system. Then the necessary and sufficient condition is proposed for the existence of the H∞filtering and an linear matrix inequality based design approach is presented for the desired filter.5. The concept of "singularly perturbed descriptor systems" is proposed and the robust stability problems for the system in both continuous-time and discrete-time cases are studied. The singularly perturbed descriptor system under considered is with both time-variant nonlinearity and small perturbed parameter. By applying the fixed-point principle and matrix inequality technique, a sufficient condition is presented via linear matrix inequality under which the solution exists and the system is globally exponentially asymptotically stable simultaneously.6. By applying bounded real lemma of linear continuous-time descriptor sys-tems and linearizing transformation technique, an linear matrix inequality based filtering design approach is presented for linear singularly perturbed descriptor sys-tems. It should be noted that the obtained results are independent of the small parameter, thus the numerical stiff problem can be avoided.