Sensitivity functions for multi-input linear time-invariant systems—II. Minimal-order models†

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Abstract
In Part I, the authors utilized frequency domain techniques to obtain low-order sensitivity models M of m-input, linear, constant, nth-order dynamic systems. The purpose of this paper is to develop a constructive approach for determining the minimal order (ρ) of M. For single-input systems it is demonstrated that ρ = n and for normal systems ρ = inn. For general systems, tight upper and lower bounds on ρ are provided. These bounds are stated in terms of the system structural properties. Procedures for synthesizing the minimal-order sensitivity models are mentioned. Examples motivate and illustrate both the key ideas and applications of the results.

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