On the Identification of Self-Adjoint Linear Time-Varying State Models

Abstract

A novel approach to the identification of linear time-varying (LTV) systems is illustrated, based on the concept of duality. Generically, if N input-output trajectories (uk, yk), k = 1,...,N of a self-adjoint LTV system are known, then the duality relation can be used to derive state trajectories xk, k = 1, ., N corresponding to such data. Such state trajectories are computed by factorizing a matrix directly constructed from input-output data of the primal and the dual system. From such input-state-output trajectories an “unfalsified” linear time-varying model can be obtained solving a system of functional equations.