Periodically Time-varying State Observer Design for Multi-rate Systems Using l₂-induced Norm

Abstract

A multi-rate state observer with a periodically time-varying gain is proposed in this paper. The proposed observer can be regarded as a periodically time-varying system. By using the cycling technique, the periodically time-varying system can be dealt with as a time-invariant system. This paper presents a method to design a multi-rate state observer using the cycling technique. Then, analysis about the l₂-induced norm of the estimation error by the proposed observer is reduced to an LMI optimization problem. Then, the design problem of the time-varying gain is also described as an LMI optimization problem. The effectiveness of the multi-rate state observer is shown by numerical examples.