Impulsive Mode Elimination for Descriptor Systems by a Structured P-D Feedback

The problem of impulsive mode elimination for descriptor systems via a structured output proportional and derivative (P-D) feedback is investigated in this technical note. The motivation of solving this problem arises from an observation that the impulse behavior for some descriptor systems can not be eliminated completely by a parameterized output P-D feedback, but it can be removed by a structured P-D feedback elegantly designed. In order to explain this phenomenon explicitly, a concept of the structured P-D feedback is first introduced, then an explicit necessary and sufficient condition is constructively derived for the closed loop systems to be regular and impulse-free by the structured P-D feedback. The main result is represented in terms of the original system parameters instead of decomposed subsystem parameters. Finally, an example is provided to illustrate the effectiveness of the proposed result.