Characteristic Multiplier Assignment in Linear Periodic Systems

Abstract

For linear periodic systems, the assignment of a set of characteristic multipliers is an important problem. Brunovsky pointed out that the necessary and sufficient condition for assigning the characteristic multipliers was the system to be completely controllable, and Kohno considered the same problem for discrete systems. But there were left some unresolved problems to implement the results. This paper discusses the necessary and sufficient condition of controllability for such systems that have analytic coefficients. Under this condition, we propose an easily programmable type algorithm for assigning a set of characteristic multipliers, where the feedback matrix is composed of a sequence of Dirac delta functions. This type of feedback is easy to implement using proper approximation to the delta function and is proved to be useful by applying it to a system governed by Mathieu equation.