Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure.
['Stéphane Azou', 'Pascale Bréhonnet', 'Pierre Vilbé', 'Léon-Claude Calvez']
A new discrete impulse response Gramian and its application to model reduction