Finite‐time functional interval observer for linear systems with uncertainties.

This study investigates the problem of designing a finite‐time functional interval observer (FTFIO) for linear systems with uncertainties. A novel structure is proposed to design an FTFIO for uncertain systems. Based on the proposed structure, the sufficient conditions for the existence of such a finite‐time observer are established as a set of coefficient matrix equations with a constraint matrix. Meanwhile, using the obtained existence conditions, the parametric expression of an FTFIO is developed by adopting the solutions to a type of first‐order Sylvester equations, which provides extra degrees of freedom. Finally, the FTFIO design method is efficiently applied to the estimation problem in two examples, including the simple numerical system and chaotic system. [ABSTRACT FROM AUTHOR]