Filtering Continuous-Time Linear Systems With Time-Varying Measurement Delay

We consider the filtering problem of LTI continuous-timesystems with known and bounded measurement delays. The aim of thepaper is the design of a finite-dimensional sub-optimal filter whose performancein terms of the estimation error is comparable to optimal infinite dimensionalapproaches. We show that the proposed approach allows fora precise characterization of the relationship between measurement delayand the covariance of the estimation error. In the time-varying case norestrictive hypotheses on the delay function are needed. The proposedfilter can therefore be applied to delay functions for which traditionalinfinite-dimensional approaches cannot be straightforwardly applied.