Computing the Kalman form

Clément Pernet (1) , Aude Rondepierre (1) , Gilles Villard (2)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 LIP - Laboratoire de l'Informatique du Parallélisme

We present two algorithms for the computation of the Kalman form of a linear control system. The first one is based on the technique developed by Keller-Gehrig for the computation of the characteristic polynomial. The cost is a logarithmic number of matrix multiplications. To our knowledge, this improves the best previously known algebraic complexity by an order of magnitude. Then we also present a cubic algorithm proven to more efficient in practice.

Mots clés: Kalman form; Keller-Gehrig algorithm; characteristic polynomial

Domaines: Calcul formel [cs.SC]; Optimisation et contrôle [math.OC]

Clément Pernet, Aude Rondepierre, Gilles Villard. Computing the Kalman form. 2005. ⟨hal-00009558v3⟩