Continuous time frequency domain LPV state space identification via periodic time-varying input-output modeling

We aim to identify a parameter-varying state space model that is suited for control design. Current LPV controller synthesis tools usually require a state space formulation that is affine in the scheduling parameters. We therefore present a frequency domain state space identification method for periodic parameter variation, in continuous time. First, we identify a periodic time-varying input-output differential equation. Next, this representation is transformed into a time-varying state space form. We use a closed-form expression for the states, consisting of binomial coefficients and derivatives of the original differential equation coefficients. Finally, an affine LPV state space model is fitted. The difficulty is to select the proper basis functions, but in this routine, we have an educated guess. Special attention is given to the sparsity and structure in the frequency domain calculations.