Algebraic State Estimation For Linear Time-varying Systems

Abstract

In this paper, we introduce a new algebraic approach for the state estimation of linear time-varying (LTV) systems. This approach is based on the following mathematical tools: Leibniz formula, generalized integration by parts, operational calculus and distribution theory. Firstly, we estimate the successive time derivatives of the measured output. Then, a generalized expression of the state variables of the system as a function of the integrals of the output and the input is obtained. Comparisons with the Kalman-type observer and some simulation results are given to illustrate the performance of the proposed approach.