Robust finite time functional observers in uncertain systems

Design of the robust finite time functional observer in uncertain linear systems is studied. Its aim is to design a robust functional observer which can estimate the state linear functions of uncertain linear systems in a predefined finite time. Based on the parametric solutions for a class of Sylvester matrix equations, 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 finite time functional observer design. By using the offered degrees of freedom, the robust indexes are parameterized and the design problem of the robust finite time functional observers is changed into a minimization problem and an algorithm to design the robust finite time functional observers for 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 the robust finite time functional observers in the uncertain linear systems.