An approach for approximating linear time-invariant system models of high order by simplified models of low order is developed. The problem of approximating systems having no unstable modes is investigated first. An iterative scheme for minimizing a quadratic fractional of the error between the system outputs and simplified model outputs is proposed. The computational requirements of the algorithm are reduced by first converting the multiple input system to an equivalent single input system and then choosing a canonical structure for the simplified model. The Schwarz canonical form is selected and advantage is taken of the special properties of the Schwarz form. The simplification of systems having unstable modes is then considered. A technique for decomposing the system model into stable and unstable subsystems is presented. The unstable modes of the system are retained in the simplified model, and the algorithm for reducing the order of stable systems is.applied to the stable subsystem. Finally, the use of simplified models in designing suboptimal output regulators for complex systems is outlined. The suboptimal control scheme is applied to the power system stabilization problem. Two examples of power.system control are given to demonstrate the value of the control scheme. / Master of Science