Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

In this paper, a parametric method to design a functional interval observer (FIO) for time-delay systems with both input and output additive disturbances is investigated. First, a novel definition and sufficient condition for the existence of an FIO are proposed. Inspired by the solution of a class of generalized Sylvester matrix equations (GSEs), completely parameterized expressions of FIO coefficient matrices are established. The parameter matrices in the expressions can be utilized as the design degrees of freedom and optimized to improve the convergence rate of the error system. Finally, a numerical example and a real-world example are presented to demonstrate the effectiveness of the proposed method.