A behavioral approach to LPV systems

Linear Parameter-Varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different models it appears that time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. In order to construct a parametrization-free description of LPV systems a behavioral approach is introduced that serves as a solid basis for specifying system theoretic properties. LPV systems are defined as the collection of valid trajectories of system variables (like inputs and outputs) and scheduling variables. Kernel, input-output, and state-space representations are introduced as well as appropriate equivalence transformations between these models.