Two-step zonotopic estimation method for discrete-time linear delayed systems

This paper deals with interval state estimation for discrete-time linear systems with known time-varying delay. The considered systems are subject to unknown but bounded disturbances and measurement noise in predefined zonotopes. The main contribution lies in the development of a two-step interval estimation method which integrates a robust observer design providing more degrees of design freedom with a zonotopic analysis technique. By introducing the H_∞ formalism in the observer design, the proposed method is effective in reducing the effects of unknown uncertainties and improving the estimation accuracy. Based on the designed observer, the interval estimation is guaranteed by a novel zonotopic analysis taking into account the effects of the time-delay on the system dynamics. By using zonotopes, the proposed approach is intuitive and is able to overcome the wrapping effects, which refers to the significant growth of the constructed set dimension in the propagation process. Numerical simulations of a two-stage chemical reactor with delayed streams are given to show the effectiveness and superiority of the proposed method.