Interval estimation of state and unknown input for linear discrete-time systems

This paper addresses the problem of state and unknown input estimation for linear discrete-time systems subject to unknown but bounded process disturbance and measurement noise. The existing methods treat this problem based on coordinate transformation, which is complex and may incorporate some conservatism. Unlike the existing methods, we estimate the state and unknown input simultaneously based on an augmented approach. Then a novel observer structure and an L_∞ norm based approach are presented to obtain a tight interval of estimation. The viability and validity of the proposed method are demonstrated by numerical simulations.