State Observers with Prescribed Output Error Bounds

Abstract

This paper presents a state observer design for continuous linear time-invariant (LTI) systems subject to unknown bounded disturbances that enforces a prescribed bound on the observer output error (residual). The proposed observer augments a Luenberger observer with state resets triggered when the residual norm reaches a prescribed bound. The reset map guarantees contraction of the residual at jump instants, forward invariance of the prescribed residual envelope, and strict decrease of the estimation-error Lyapunov function at every reset, while preserving the uniform boundedness properties of a standard Luenberger observer. Notably, the observer design does not require knowledge of the disturbance bound. Simulation results confirm the analysis: the residual remains within the prescribed bound, whereas a standard Luenberger observer with the same gains violates this bound.