Study On Some Issues Of Robust Region Stability For Uncertain Systems

A dynamic system is called R -stable, if all poles of the system are located in a region R belongs to left-half complex plane. In engineering practice, an R -stable system usually possesses many nice properties, such as stability, rapid convergence and the steadiness of switch systems. Therefore the problem of R -stability of dynamic systems has been an attracting issue for many control researchers. Into the bargain, there exist inevitably uncertainties for the dynamic system in the practical industrial process control. These uncertainties can be divided into two kinds. The one is non-structuring uncertainties, such as un-modeled dynamics, change of systems environment, existence of nonlinear components and external disturbances of systems, etc. The other is structuring uncertainties, such as parameter uncertain system model, etc. The structuring uncertainties, according to the state of research, can be divided into norm-bounded uncertainties, convex combination uncertainties and interval uncertainties, etc. To guarantee the dynamic systems suffered from disturbance of uncertainties to be R -stable and possess some dynamic performance, it looks more necessary to study the robust R-stability. Moreover, because of transmission process, large-lag links and complicated on-line analyzer etc, a large number of industrial processes (metal engineering, chemical engineering systems, biomedical systems and so on) can be modeled as time-delay systems and systems stability and performance are always dominated by delay phenomena. So the studies of R-stability and the design of corresponding controller for delay systems are also important in academic research and engineering application.In this paper, the problem of robust R -stability analysis, including robust α -stability and disk stability, is studied. The dynamic system considered in this paper is linear system with norm-bounded uncertainties or linear time-delay system with norm-bounded uncertainties or linear parameter-varying delay system or fuzzy Takagi-Sageno system, etc. Lyapunov-Razumikhin stability theorem, linear matrix inequality technique, matrix analyzing methods and convex programming theory are adopted in this paper. For the dynamic systems mentioned above, it is designed that the output feedback controller, or reliable controller, or state feedback controller with variance constraint which guarantees the closed-loop system to be R -stability andpossess H performance in this paper. The main contents are as follows.1. The analysis and synthesis problems of robust -stable H dynamic output feedback controller for a class of linear uncertain time-delay systems are considered. A sufficient condition for -stability and H performance of the systems is derived and the corresponding dynamic output feedback controller was constructed by linear matrix inequality approach.2. The synthesis problem of output-feedback control law subjected to robust a -stability is studied for a class of uncertain linear time-delay systems. The output-feedback controller is designed which ensures the closed-loop system to be a -uniform asymptotic stable and possess H performance index. Based on Lyapunov stability theorem, an existence condition of the controller is obtained in the state space. Applying the technique of orthogonal complement space and Schur complement lemma, the design approach of controller is proposed in terms of linear matrix inequality and the obtained linear matrix inequalities can be solved easily by Matlab toolbox.3. The design problem of robust stable H state feedback controller for a class of linear parameter-varying systems with time-delay is addressed. A sufficient condition for the existence of robust a -stable H state feedback controller is derived based on a new method and the corresponding construction method of the controller is given.4. A necessary and sufficient condition of quadratic -stability for a class of uncertain linear systems is presented in terms of linear matrix inequalities. The validity and less conservatism of the...