Fast state estimation in linear time-invariant systems: an algebraic approach

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