A biased continued-fraction expansion for model reduction of continuous-time systems

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Abstract
A mixed Cauer-type continued-fraction expansion which takes the Cauer first form and Cauer second form in a ‘biased’ feature is introduced to obtain reduced models for continuous-time systems. A new algorithm is proposed for computing the partial quotients of this biased continued-fraction expansion (BCFE) from a given general state-space model directly without having to determine its corresponding transfer function. The state-space realization of the BCFE of the transfer function is derived and the corresponding canonical state-space model is established. Two similarity transformation matrices are derived: one transforms a state-space model from a general form to a BCFE form, and the other transforms a state-space model in a phase-variable form to a BCFE canonical form. The reduced models may be biased in the sense that they may approximate the initial transient response of the original system more closely than the steady-state response, and vice versa. Given the desired order of reduced model, the BCFE method gives a family of reduced models which approximate the original system. Examples are provided to illustrate the algorithms.