Integrated state/disturbance observers for two-dimensional linear systems

In this study, the problem of simultaneous estimation of system states and disturbances is addressed for two-dimensional (2D) linear systems. The considered 2D systems can be described as Fornasini-Marchesini second local state-space model coupled with unknown disturbances in the measurement equation. Asymptotically stable and uniformly ultimately bounded integrated state/disturbance observers are proposed as solutions to the simultaneous estimation problem under different system conditions. For the asymptotically stable integrated state/disturbance observer, a necessary and sufficient condition for its existence is presented and proved. For the uniformly ultimately bounded integrated state/disturbance observer, a sufficient condition for its existence is given and proved, and it can be designed such that its estimation error has arbitrarily small upper bound. Moreover, some constructive design methods are given for the proposed integrated state/disturbance observers. Finally, a thermal process plant and another numerical example are provided to illustrate the effectiveness of the proposed methods.