Two-dimensional Singular System Is Extended Roesser Models H_ ¡Þ Control And Filtering

This paper studied H_∞control problems, H_∞filtering problems as well as positive real control, the minimum energy control of the 2-D extended singular Roesser model. 2-D extended singular Roesser model mentioned above is a particular case of the general singular model of 2-D systems. This class of systems includes all the systems resulted from the linear state transformations of 2-D singular Roesser models.First of all, we studied H_∞control problems of the 2-D extended singular Roesser model and gave a sufficient condition of existence for dynamic output feedback controller. Secondly, we studied H_∞filtering problems of the 2-D extended singular Roesser model, designed a dynamical output feedback controller to achieve asymptotic stability and H_∞performance. The 2-D H_∞filtering problem is investigated for both the 2-D filters of an observer-based structure and a general form. We gave a sufficient condition based on the LMI. Third, we studied positive real control problems of the 2-D extended singular Roesser model. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We obtained a sufficient condition for the existence of the desired output feedback controllers in terms of LMI. Fourth, we studied minimum energy control of the 2-D extended singular Roesser model, found a sequence of input u(i,j) which transfers extended singular Roesser model from the initial local state to the desired final local state. In addition, we considered the problem of the guaranteed cost control for a class of two-dimensional discrete systems described by the Roesser model. A linear matrix inequality (LMI)-based criterion for the existence of robust guaranteed cost controller is established. Such controller renders the closed-loop system asymptotically stable for all admissible uncertainties and guarantees an adequate level of performance. We gave a sufficient condition for the existence of the desired output feedback controllers. These conclusions are based on the LMI, therefore it very convenient for computer demonstration. Finally, we provide a numerical example to demonstrate the applicability of the proposed approach in each section.