Observer Design for Singularly Perturbed Systems With Multirate Sampled and Delayed Measurements

Abstract

This paper considers observer design problem of singularly perturbed systems (SPSs) with multirate sampled and delayed measurements. The outputs are classified into two sets which are measured at different sampling rates and subject to transmission delays. The error system is modeled as a continuoustime SPS with a slowvarying delay and a fastvarying delay. A new Lyapunov functional taking the delay properties into account is constructed. Based on the Lyapunov–Krasovskii functional, sufficient conditions for stability of the error system are proposed by which an observer design method is proposed. A realistic example is used to illustrate the obtained results.