α-Decay rate observer design for linear systems with delayed state

In this paper, the problem of designing an observer for linear systems with delayed state with the property that the estimated error converges to zero with a prespecified decay rate a is considered. A Luenberger-type observer for linear systems with delayed state is firstly proposed then, under certain observability conditions on the delayed-state system, criteria are proposed to ensure the a-convergence of the estimated error. Two examples are given in order to illustrate the proposed methods.