Impulse Eliminations for Rectangular Descriptor Systems: A Unified Approach

Descriptor systems, in general, have impulses in their solutions and do not admit arbitrary initial conditions. In this letter, we design a unified proportional state feedback controller for rectangular descriptor systems such that the closed-loop system has no-impulsive modes if the system is impulsive-mode controllable. Further, the closed-loop system will have no-impulsive modes and admits arbitrary initial conditions provided that the system is impulse controllable. Additionally, some other equivalent algebraic criteria for impulse controllability are also deduced. Real-life models from robotics and electrical systems are given to illustrate the theory.