Analysis of Impulsive Modes in Kronecker Canonical Form for Rectangular Descriptor Systems

Unlike regular descriptor systems, there are various notions for impulse freeness in rectangular linear descriptor systems. Descriptor systems, in general, do not admit arbitrary initial conditions. In this note, conditions for having no impulsive modes, free of impulse, and admitting arbitrary or particular initial conditions are analyzed by deriving their respective Kronecker canonical forms for rectangular descriptor systems. Some other equivalent conditions are also discussed. Numerical examples are presented to illustrate the theory.