A singular perturbation canonical form of invertible systems: determination of multivariate root-loci

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Abstract
A new canonical form of multivariable invertible systems is given. This form is suitable for the singular perturbation analysis of such singular problems as multi-variable asymptotic root-loci under high-gain feedback, cheap control, state variable estimation with weak measurement noise, etc. Appropriate selection and decomposition of state variables into slow and fast changing groups is a key feature that loads to well-defined singular perturbation models. The selection of state variables is accomplished without explicitly calculating any eigenvalues of the given system but by knowing the direct relationship of the output and its differential coefficients with the input. The use of the canonical form to characterize the multivariable root-loci under high-gain feedback is demonstrated.