Design of a Multi-rate State Feedback Gains for Disturbance Rejection in Multi-rate Systems with Long Input Periods

Abstract

In this paper, we consider a control system design problem for multi-rate systems with long input periods. The proposed control system can be regarded as a periodically time-varying system. Then, the periodically time-varying system can be dealt with as a time-invariant system by using the cycling technique. This paper presents a method to design multi-rate state feedback gains for disturbance reduction. Then, analysis about the l₂-induced norm from the disturbance to the output with the proposed multi-rate state feedback gains is reduced to an LMI optimization problem. Then, the design problem of the time-varying gains is also described as an LMI optimization problem. The effectiveness of the multi-rate state feedback control is shown by numerical examples.