Robust Unknown Input Observer Design for Uncertain and Noisy OSL-QIB Nonlinear Systems

In this paper, the problem of designing a robust unknown input observer (RUIO) for quadratically inner bounded (QIB), one-sided Lipschitz (OSL) nonlinear systems in the presence of noise and unknown inputs is addressed. This RUIO is formulated as a convex optimization problem where parameter uncertainty and noise are considered. Sufficient conditions for observer gain synthesis are shown to be equivalent to solving a finite set of Linear Matrix Inequalities (LMIs) and a Linear Matrix Equality (LME). Two illustrative examples, a bioreactor for biomass production from substrate consumption and a robot manipulator, are used to test the effectiveness of the approach in the presence of unknown inputs, parameter uncertainty, and measurement noise.