LINEAR PARAMETER VARYING SYSTEMS: A GEOMETRIC THEORY AND APPLICATIONS

Linear Parameter Varying (LPV) systems appear in a form of LTI state space representations where the elements of the A(ρ), B(ρ), C(ρ) matrices depend on an unknown but at any time instant measurable vector parameter ρ ∈ P. This paper describes a geometric view of LPV systems. Geometric concepts and tools of invariant subspaces and algorithms for LPV systems affine in the parameters will be presented and proposed. Application of these results will be shown and referenced in solving various analysis (controllabilty/observability) problems, controller design and fault detection problems associated to LPV systems.