Fast state estimation in linear time-varying systems: An algebraic approach

In this note, an algebraic approach for state estimation of linear time-varying (LTV) systems is introduced. This approach is based on the following mathematical tools: Laplace transform, Leibniz formula, operational calculus and distribution theory. A generalized expression of the state variables as a function of the integrals of the output and the input is obtained. The example of a DC motor system and some simulation results are given to illustrate the performance of the proposed approach.