State Observers for Linear Systems with Prescribed Residual Bounds
For control engineers needing guaranteed observer error bounds under bounded disturbances, this provides a method to enforce a prescribed residual bound, though it is an incremental modification of existing observers.
This paper proposes a state observer for continuous LTI systems with bounded disturbances that enforces a prescribed bound on the observer residual by augmenting a Luenberger observer with state resets. Simulations show the residual stays within the bound, unlike a standard Luenberger observer with the same gains.
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 residual. The proposed observer augments a continuous-time Luenberger observer with state resets, triggered when the norm of the residual equals a pre-specified bound. The reset map guarantees contraction of the residual at jump instants while preserving the uniform boundedness properties of a standard Luenberger observer. The paper also establishes forward invariance of the residual envelope and non-expansiveness of the estimation error in a Lyapunov metric. Simulation results confirm the analysis. Under bounded disturbances, the residual stays within the prescribed bound. A standard Luenberger observer with the same gains violates this bound.