Interval estimation for discrete-time linear systems: A two-step method

Abstract

This paper proposes a two-step interval estimation method for discrete-time linear systems by integrating robust observer design with reachability analysis. The proposed method is designed based on a new observer structure which can provide more degrees of design freedom. For improving estimation accuracy, H∞ technique is used in observer design to attenuate the effects of disturbances and noise. Based on the obtained observer, interval estimation can be achieved via reachability analysis. The proposed method provides an intuitive design paradigm for interval estimation and is effective in controlling the wrapping effect, which refers to the additional growth of the constructed sets resulting from the propagations of overestimations at each step. Simulation results are given to demonstrate the performance of the proposed method.