The Tie Canonical Structure Theorem

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 17 in State Space and Input-Output Linear Systems, 1998, pp 208-218 from Springer

Abstract: Abstract The development in the preceding four sections suggests that the state space of an arbitrary m -input, i -output state space linear system is composed of several kinds of states; some states, it would seem, have more influence on the input-output behavior of the system than others. It is the purpose of the present section to formulate this idea precisely. The principal result, which has become known as the Canonical Structure Theorem, was first stated and proved by [Kalman] in the well-known paper [Kalman]; the proof presented here rests heavily on the vector sum and direct sum constructions (c.f. §5) along with the reachability and observability results of §§13–16.

Date: 1998
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DOI: 10.1007/978-1-4612-3816-4_18

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