Realization Theory for LPV State-Space Representations with Affine Dependence

Mihaly Petreczky (1) , Roland Toth (2) , Guillaume Mercère (3)

1 SyNeR - Systèmes Non Linéaires et à Retards
2 TU/e - Eindhoven University of Technology [Eindhoven]
3 LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219]

We present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA). We show that minimality of LPV-SSAs is equivalent to observability and span-reachability rank conditions, and that minimal LPV-SSAs of the same input-output map are isomorphic. We present necessary and sufficient conditions for existence of an LPV-SSA in terms of the rank of a Hankel-matrix and a Ho-Kalman-like realization algorithm.

Domaines: Automatique / Robotique

Mihaly Petreczky, Roland Toth, Guillaume Mercère. Realization Theory for LPV State-Space Representations with Affine Dependence. IEEE Transactions on Automatic Control, 2016, 62 (9), pp.4667-4674. ⟨10.1109/TAC.2016.2629989⟩. ⟨hal-01406805⟩