Representations With Constant System Matrices of Linear Time-Periodic Dynamical Systems

In the paper it is investigated, under which conditions a time variable state transformation can be used to change a periodic autonomous system realization into a form with constant real coefficients. Conditions for the transformation to be periodic are further considered, and it is shown that the necessary and sufficient condition to meet the conditions is in that two specific matrices must be similar to each other. The properties of the matrices and the transformation are studied, and the discussion is then extended to input-output systems. An approach to design stabilizing control laws for these kinds of periodic systems is outlined.