On-line detection of minimal order for linear piecewise stationary systems

Abstract

This work deals with the detection of minimal order for linear systems with piecewise constant coefficients. In this case, it is impossible to use off-line algorithms. We propose, here, a real-time method able to detect the minimal order of a linear system. The basic mathematic tool is given by a simple divisibility condition of the charateristic polynomial of the differential equation for stationary systems. This necessary and sufficient condition is used to define an algorithm able to give the reduced equation. Then, we show that this result can be directly extended to linear piecewise stationary systems for which we search a change if the order. The real-time method that we obtain, is checked in simulation on deterministic systems and on systems with measured noisy informations.

Membre du GRECO Traitement du Signal et des Images