Design of robust finite time functional observers in uncertain linear systems

Abstract

In this paper, a design problem of the robust finite time functional observers in the uncertain linear systems is investigated. The aim is to design a robust functional observer which can estimate the state linear functions of the uncertain linear systems almost in a predefined finite time. Based on the parametric solutions for a class of Sylvester matrix equation, this paper presents the parametric expressions of all the gain matrices for the finite time functional observers in the linear systems without uncertainties, in which the free parameters can offer all the design degrees of freedom needed in the robust control system design. By using the offered design degrees of freedom, the robust indexes can be parameterised and the design problem of the robust finite time functional observers for the uncertain linear systems can be changed into a minimisation problem with some constraints. By solving the changed minimisation problem, a corresponding algorithm to design the robust finite time functional observers in the uncertain linear systems is proposed. Finally, a numerical example and its simulation results show the simplicity and effectiveness of the proposed design method of robust finite time functional observers in the uncertain linear systems.