Implementation of Kalman filter algorithm on reduced models using Linear Matrix Inequality method and its application to measurement water level

Abstract

This paper presents the model reduction and estimation of the state variables of the water level system using the Linear Matrix Inequality (LMI) method and the Kalman filter algorithm. We assume the system is asymptotic stable, controllable and observable, then we reduce it by LMI method. The reduced system obtained is a system that remains asymptotic stable, controllable, and observable. The reduction error using LMI method is smaller than the reduction error using Balanced Truncated (BT) method and Singular Perturbation Approximation (SPA) method. Next, we implemented the Kalman filter algorithm in the original system and the system was reduced by LMI method.