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Summary: TECHhTXL NOTES AND CORRESPONDENCE 745
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Cyclicity and Controllabilityin Linear
Time-Invariant Systems
P. J. ANTSAKLIS
Absrma-A number of results, involving the notions of contrdlability
(observability) and cyclicity in a hear time-invahnt control system, are
derived using a new basic theorem. New tests of cyclicity and contrdlabil-
ity (observabiity),together with new algorithms to evaluate the controlla-
ble (-able) modes and the minimalpolynomial are also presented.
I. INTRODUCTION
The controllability (observability) of a linear time-invariantsystem
{A , B ) and the cyclicity of a square matrix A havebeen dealt with
extensively in the literature in recent years, and many important proper-
ties have been shown using a variety of methods. In this paper, a basic
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