Cauer continued-fraction expansion about s=0 and s=a for biased reduced-order state space models

Abstract

A method of linear-system reduction is presented which produces biased state-space models such that combinations of retained time-moments and weighted time-moments may be varied. The method is based on the concept of representing the system transfer function in a biased Cauer form of continued-fraction expansion (CFE) about s = 0 and s = a. A new algorithm for obtaining the continued-fraction expansion of the transfer function of a linear time-invariant system from its state-space model directly, without first determining the corresponding transfer function, is derived. A realization which uses only integrators for the biased Cauer continued-fraction expansion about s = 0 and s = a is presented. The corresponding canonical state-space model is established, which allows the reduced-order state-space model to be formed by directly partitioning the system matrices. Also presented are two new similarity transformation matrices; one is used to transform a state-space model from a general form to a state-space model in the biased CFE canonical form, and the other is used to transform a state-space model from phase-variable canonical form to the biased CFE canonical form.