Characteristic Multiplier Assignment for Periodic Systems by Multirate Sampled State Periodic Hold Control

Abstract

This paper proposes a method of characteristic multiplier assignment of linear ω-periodic continuous time systems by “multirate sampled state periodic hold (MSSPH)” control.
In “sampled state periodic hold (SSPH)” control presented by Kabamba, the sampling interval has to be equal to ω. On the contrary, in MSSPH control, sampling instants chosen arbitrarily can be added within one period. It is shown that the system discretized by MSSPH control is reachable if and only if the original system is controllable.
On the basis of the eigenvalue assignment problem in periodic discrete-time systems, it is shown that the characteristic multipliers can be assigned iff the open-loop system is controllable, and under an additional assumption the whole monodromy matrix is assignable.This method is illustrated by a numerical example.