Finite Horizon Approximation of Linear Time-Varying Systems

Abstract

We consider the problem of approximating a linear time-varying p X m discrete-time state space model S of high dimension by another linear time-varying p X m discrete-time state space model Š of much smaller dimension, using an error criterion defined over a finite time interval. We derive the gradients of the norm of the approximation error and show how this can be solved via a fixed point iteration.