State and output feedback regularization for descriptor systems by Kalman canonical form

The problem of state and output feedback regularization for descriptor systems by Kalman canonical form is investigated. First we give the Kalman canonical form for the descriptor systems, by which structure, the regularization and the impulsive mode elimination can be conveniently explored. Then necessary and sufficient conditions are given for the closed loop system to be regular and impulse-free by a parameterized state or output feedbacks. Furthermore, a structured output P-D feedback is considered and a necessary and sufficient condition for the closed loop systems to be regular and impulse-free by the structured output P-D feedback control is presented. The main results are given in terms of subsystem parameters by the Kalman canonical form, in which the structure of system matrix is revealed. Finally, an example is provided to illustrate the correctness of the theory.