Static Output Feedback Control For Delta Operator Systems

The problems of static output feedback control for the Delta operator formu-lated systems are studied. Based on the Lyapunov stability theory and the linear matrix inequality (LMI), the performance of the system is researched in this pa-per. Meanwhile, the new sufficient conditions, which meet the system performance requirements are given. Furthermore, the design methods of the static output feed-back controller are presented. Numerical examples are used to test and verify the availability and effectiveness of the design methods. The main content of this paper is divided into the following three parts:(i) H∞ control problems for the Delta operator formulated uncertain systems are studied. The new condition of robust stability of the system with H∞ per-formance is given for the Delta operator systems with norm bounded parameter uncertainty. Furthermore, the design method of the static output feedback robust H∞ controller is presented.(ii) Researching the guaranteed cost control problem of the static output feed-back delta operator system with convex polyhedron uncertainties. The new condi-tion of robust stability of the system with guaranteed cost control is given for Delta operator systems with convex polyhedron uncertainties. Furthermore, the design method of the static output feedback guaranteed cost controller is presented based on this new condition.(iii) Researching the problems of static output feedback control for the Delta operator formulated time-varying delay systems. The new condition of robust stabil-ity for the Delta operator formulated time-varying delay systems is provided. Then, based on this, a design method of the static output feedback controller is presented.