Robust Proportional Integral Filter Design for Linear Discrete-Time Uncertain Systems

The problem of simultaneous robust fault and state estimation for linear discrete-time systems with bounded uncertainties is discussed in this paper. To solve this problem, a design approach to the robust proportional integral filter (RPIF) is developed. Based on the robust least-square estimation method, new robust filters (RPIF) guaranteeing an optimized upper bound for any allowed uncertainty are proposed for linear uncertain systems. The unknown additive fault affects both the state and the output equations without any prior information about his dynamical evolution. In this study, the filter parameters are determined by solving a convex optimization problem subject to linear matrix inequality. The effectiveness of the proposed results are demonstrated through an illustrative example that gives a robust simultaneous fault and state estimation for linear uncertain systems.