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Conference Proceedings
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3rd IFAC Workshop "PERIODIC CONTROL SYSTEMS" (PSYCO'07)
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On Kalman Canonical Decomposition of Linear Periodic Continuous-Time Systems with Real Coefficients
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In this note, structural decomposition of linear periodic

continuous-time systems is discussed. A fundamental problem to decompose a state of a periodic system into controllable and uncontrollable parts is conjectured to be achieved by a

continuously differentiable and periodic coordinate transformation with the same period of the system, however there is a counterexample to this conjecture. Hence we derive a condition for the existence of such a coordinate

transformation. We also prove that, by relaxing a class of coordinate transformation, it is always possible to construct a periodic coordinate transformation with the double period of the periodic system.

continuous-time systems is discussed. A fundamental problem to decompose a state of a periodic system into controllable and uncontrollable parts is conjectured to be achieved by a

continuously differentiable and periodic coordinate transformation with the same period of the system, however there is a counterexample to this conjecture. Hence we derive a condition for the existence of such a coordinate

transformation. We also prove that, by relaxing a class of coordinate transformation, it is always possible to construct a periodic coordinate transformation with the double period of the periodic system.