Reduced Order Observer for Linear Time-Invariant Multivariable Systems with Unknown Inputs

This paper presents the design of a new reduced order observer to estimate the state for a class of linear time-invariant multivariable systems with unknown inputs. The proposed design approach is a combination of the approaches proposed by Hou and Muller (IEEE Trans. Autom. Control 37:871-875, 1992) and Boubaker (Int. J. Autom. Control Syst. Eng. 5:45-51, 2005); matrix decompositions, state transformations, and substitutions based on coordinate changes are used. It is shown that the problem of reduced order observers for linear systems with unknown inputs can be reduced to a standard one (the unknown input vector will not interfere in the observer equations). The effectiveness of the suggested design algorithm is illustrated by a numerical example (aircraft lateral motion), and, for the same aircraft dynamics, we compare our new observer with other already existing observers from the existence conditions and dynamic characteristics point of view; the superiority of the new designed observer is demonstrated.