Non-Asymptotic State Estimation for Linear Time-Varying Systems with Multi-Outputs

In this article, a non-asymptotic and robust state estimator is proposed for linear time-varying systems with multi-outputs. Firstly, an algorithm for the transformation matrix's construction is developed. Then, based on the designed transformation matrix, the considered system is transformed into an observable canonical form via the change of coordinates, which is different from the existing ones. Additionally, by employing the modulating functions method to the obtained canonical form, the state estimation is reached by means of algebraic integral formulas which are robust against corrupting noises and independent of the system's initial value. Moreover, the outputs and their derivatives can also be estimated. Finally, a simulation example is provided to demonstrate the validity of the proposed estimation method.