Maximum parametrization of the set of all solutions to linear periodic systems

Abstract In the Floquet representation theorem, a state transition matrix whose second argument is 0 is represented as a product of a real-valued periodic matrix function and a real-valued matrix exponential function. In contrast, we have proposed a novel representation as a product of a real-valued periodic matrix function and two real-valued matrix exponential functions. In this note, the structure of the previously proposed representation is intensively investigated in terms of the maximum parametrization.

[1]  Raymond J. Spiteri,et al.  Real Floquet factors of linear time-periodic systems , 2003, Syst. Control. Lett..

[2]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[3]  G. Floquet,et al.  Sur les équations différentielles linéaires à coefficients périodiques , 1883 .

[4]  Jorge Angeles,et al.  Pitfalls of a least-squares-equivalent controller for linear, time-periodic systems , 2001 .

[5]  Ichiro Jikuya,et al.  A Floquet-like factorization for linear periodic systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.