New Finite-Time and Fast Converging Observers With a Single Delay

Abstract

We provide new reduced order observer designs for a key class of nonlinear dynamics. When continuous output measurements are available, we prove that our observers converge in a fixed finite time in the absence of perturbations, and we prove a robustness result under uncertainties in the output measurements and in the dynamics, which bounds the observation error in terms of bounds on the uncertainties. The observers contain a dynamic extension with only one pointwise delay, and they use the observability Gramian to eliminate an invertibility condition that was present in earlier finite time observer designs. We also provide analogs for cases where the measurements are only available at discrete times, where we prove exponential input-to-state stability. We illustrate the advantages of our new observers using a DC motor dynamics.