Multi-objective robust ℋ∞ observer design for one-sided Lipschitz nonlinear uncertain systems

In this paper, the problem of robust ℋ_∞ observer design for one-sided Lipschitz nonlinear systems in the presence of time-varying parametric uncertainties is addressed. The main idea is to minimize the ℒ₂ gain from the disturbance to the state estimation error and at the same time the admissible one-sided Lipschitz constant is to be maximized. In addition to asymptotic convergence, the designed observer also ensures robustness against disturbances, parametric uncertainties and additive one-sided Lipschitz nonlinear uncertainty. The solution is represented in terms of LMIs which enables us to carry out the design procedure using Matlab LMI toolbox making the nonlinear observer design an easy task.