A new discrete impulse response Gramian and its application to model reduction

S. Azou (1) , Pascale Bréhonnet (1) , P. Vilbe (1) , L.C. Calvez (1)

1 LEST - Laboratoire d'Electronique et Systèmes de Télécommunications

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.

Mots clés: Reduced order systems; Read only memory; Equations; Controllability; Observability; Frequency; Continuous time systems; Polynomials; System identification; Delay

Domaines: Traitement du signal et de l'image [eess.SP]

S. Azou, Pascale Bréhonnet, P. Vilbe, L.C. Calvez. A new discrete impulse response Gramian and its application to model reduction. IEEE Transactions on Automatic Control, 2000, 45 (3), pp.533 - 537. ⟨10.1109/9.847738⟩. ⟨hal-01508752⟩