Impulse analysis in Kronecker form and impulse elimination for rectangular descriptor systems

Abstract

Contrary to regular descriptor systems, there are various notions for impulse freeness and impulse controllability for rectangular linear descriptor systems. Moreover, rectangular descriptor systems generally do not have solutions for arbitrary initial conditions. This paper studies the conditions for free of impulse, and no impulsive modes admitting arbitrary initial conditions in the form of Kronecker canonical form (KCF) along with other equivalent and geometric conditions. The knowledge of KCF blocks significantly simplifies the analysis of the system solutions. Further, conditions for impulse controllability are investigated, and a proportional state feedback is designed such that the closed-loop system has no impulsive modes and admits arbitrary initial conditions. This makes the system solutions smooth without any restrictions on initial conditions. Physical and academic instances are provided to fortify the theory.