Uniform Approximation of Linear Systems

In the analysis and design of control systems it is often useful to have low order constant coefficient models for the system. The problem of modeling linear systems by lower order linear systems has received considerable attention, but these analyses have usually been restricted to the modeling of constant coefficient systems. References 1 through 5 contain various approaches to the system approximation problem; however, these analyses are generally restricted to the modeling of constant coefficient systems or systems which are forced with a given input or initial condition. The control system analyst often finds himself dealing with nonstationary systems, but little work has been done in the area of optimally modeling this class of systems. The emphasis here is on modeling the class of linear, homogeneous time-varying systems with constant coefficient models. Reference 6 considers approximation of forced systems. Rather than design the model requiring solutions of the actual and approximate systems be "close" for a prescribed initial * From a dissertation written as part of the requirements for a Ph.D. degree, New York University, 1968. 209