On the application of the {1}-inverse to the design of general structured unknown input observers

This paper presents a concise and straightforward formulation of the unknown input observer (UIO) problem based on the general structured observer. By employing the simplest generalized inverse of matrices, the {1}-inverse, we develop constructive design procedures for the UIO design that provide necessary and sufficient conditions for both full-order and reduced-order general structured UIOs. Moreover, corresponding configurations for continuous-time systems are also derived, and consequently this paper renders the complete solutions for general structured UIO design. Furthermore, we show that the general structured UIO is structurally and numerically equivalent to the UIO in the configuration of Luenberger observer. Examples are included to illustrate the validity of the proposed methodology.