Abstract
Commencing with linear system models which are matrix polynomial equations in a differentiation or delay operator, it is shown how to obtain a set of equivalent first-order equations which are consistent, independent, and complete in precisely-defined senses. In contrast to state-space equations, the resulting system has a symmetric representation of inputs and outputs, and admits of canonical forms from which the parameters of the (possibly improper) transfer-function matrix are obtainable by inspection. As a result, the representation is extremely useful for system identification, inversion, signal-flow graph manipulations, and other applications. Included are methods for producing the required representation if it is possible, as well as the elimination of extraneous variables, and tests for constraints on independent variables and for unique solutions. Only elementary row and column operations on a new form of system matrix are used.
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