On the theory of linear dynamic system with periodic parameters

This paper presents an extension of the classical theory of Floquet to provide a unified treatment on the state transformation properties and stability of linear dynamic systems with continuous and piecewise continuous periodic parameters. The linear dynamic system with periodic parameters is represented mathematically by a linear differential equation with periodic coefficients.It is shown that the linear differential equation with periodic coefficients can always be reduced to linear difference equations with constant coefficient matrices. The coefficient matrices of difference equations are all related to each other by similarity transformations. Consequently, it is sufficient to study any one of the difference equations to determine stability of the original differential equation with periodic coefficients. The entire discussion is developed from the point of view of the state transformation which has been proven to be of great use in the study of dynamic systems