A reduced order state observer design procedure for multivariable linear time-invariant systems is developed. The procedure is based on the eigenstructure assignment approach. A compact form for the obsever gain matrix is derived according to any arbitrary prespecified set of eigenvalues and eigenvectors. A set of free (design) parameter vectors is required upon which the eigenvector assignability is determined. In case of having observer dynamics of order equal to or less than the number of system outputs. complete assignability can be achieved. Having such a reduced order observer in a feedback loop. the choice of the free parameters in order to reduce the impact of the initial mismatch between the system states and the corresponding estimates is derived. The approach developed is applied to minimize the effect of external gust on the lateral axis of L-1011. aircraft at cruise flight condition .