Abstract
A new, relatively simple, constructive method is presented for obtaining state-space or normal form representations for linear, time invariant systems whose dynamics are expressed in a more general matrix differential operator form. The development employed provides new insight into various structural properties of linear systems. Equivalence is defined for a rather large class of linear systems, and an algorithm is given for reducing any member of this class to normal form. In order to outline the algorithm, a number of “well known” results involving polynomial matrices are employed for the first time, along with the “structure theorem”. An example is used to illustrate the algorithm and two appendices are employed to clarify the development.
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