Robust $\Hinf$ Observer Design via Finsler's Lemma and IQCs
This provides a more robust observer design method for control engineers dealing with uncertain systems, though it is an incremental improvement over existing LMI-based approaches.
The paper tackles robust H-infinity observer design for systems with block-structured uncertainty by developing a Finsler-based LMI formulation that relaxes coupling constraints, addressing limitations like infeasibility for marginally stable dynamics and wide uncertainty ranges. It demonstrates the approach on quaternion attitude estimation and mass-spring-damper systems, showing improved feasibility.
This paper develops a Finsler-based LMI for robust $\Hinf$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement $\He{PA} \prec 0$ (which fails for marginally stable dynamics), and a multiplier--Lyapunov trade-off that causes infeasibility for wide uncertainty ranges. For marginally stable dynamics, artificial damping in the design model balances certified versus actual performance. The framework is demonstrated on quaternion attitude estimation with angular velocity uncertainty and mass-spring-damper state estimation with uncertain physical parameters.