Optimal H₂ filtering for measurement‐delay systems with multiplicative noise and sampled data

Abstract

This paper is concerned with the optimal H 2 filtering problem for continuous-time systems with multiplicative noise and multiple sampled delay measurements. The reorganized observation technique is firstly applied for treating the sampled delay terms, and then an equivalent delay-free sampled measurement is received. An optimal H 2 filter is constructed by using a dynamic model with finite jumps, which can provide the state estimation of the measurement sampling interval as well as the measurement sampling moments. The filter gain is given in terms of the stabilizing solution to a set of specific Riccati differential equations. It should be pointed out that no state augmentation is required, and thus the Riccati equation developed in this paper remain the same dimension as that of the original system state. This is the clear distinction from the state augmentation method. A practical example is finally supplied to illustrate the efficiency of the proposed results.