Uniform approximation of linear systems

A method for reducing the complexity of the class of linear, time-varying, dynamic control systems is developed where the approach taken is that of uniform approximation (that is, modeling for a region of initial conditions). The objective of the modeling procedure is to choose a linear time-invariant system of given dimension, that minimizes a “worst-case” type of error criterion. Some results from the theory of widths of sets in Banach space are used to obtain bounds on the optimal approximation error as a function of the dimension of the approximating system. The use of these bounds in choosing the order of the approximation is discussed. An example illustrates the use of the derived results.