Static Output Feedback Control For Descriptor Systems

Stability is a primary issue of a variety of control problems whether general systems or singular systems. The goal of control is to make the system stable. In recent years, stabilization of control systems via state space methods have made great progress whether in theory or engineering applications. The state feedback control and the dynamic output feedback control are the main meth-ods in theory, but they are not usually feasible in practical situations. Taking into account the cost, system reliability and other factors, it is more appropri-ate to choose a static output feedback controller if it can achieve closed-loop system performance requirements. Therefore, the study of the static output feedback have received a lot of attentions. The author found that the main results obtained yet refer to linear time-invariant systems, there is indeed rare literature on the static output feedback for singular systems.The static output feedback control problem is investigated in this paper for continuous descriptor systems and discrete descriptor systems. New nec-essary and sufficient conditions are established to ensure the admissibility of the continuous descriptor systems. The form of the decision theorem obtained in the paper looks complicate compare with the former, but it is convenient to the design of controller. Then, based on the new necessary and sufficient conditions, sufficient conditions are derived for the exist of the controller. The controller can be derived directly via the cone complementarity linearization techniques. All the results of the continuous cases are parallel to that of the dis-crete cases. New necessary and sufficient conditions are established to ensure the admissibility of the discrete descriptor systems. Sufficient conditions are also derived for admissibility of the discrete closed-loop systems. The static output feedback can also be derived directly via the cone complementarity linearization techniques. Finally, illustrative examples are presented to demon-strate the effectiveness of the proposed approaches.