Canonical Forms in Problems of Estimation

Abstract

The methods of solving the problems of estimation based on the identification and Jordan canonical forms are suggested. The interval observer, virtual sensor, and sliding mode observer design problems are considered. The methods to solve these problems are developed both for the continuous-time and the discrete-time linear systems under the external disturbance and measurement noise. All the developed methods are based on the reduced order model of the original system invariant with respect to the disturbance. It is shown that the identification canonical form is the best way to solve the problem for the discrete-time systems while Jordan canonical form for the continuous-time systems.