State observer synthesis by measurement results for nonlinear Lipschitz systems with uncertain disturbances

We propose ways to synthesize state observers that ensure that the estimation error is bounded on a finite interval with respect to given sets of initial states and admissible trajectories and also simultaneous $H_\infty$-suppression at every time moment of initial deviations and uncertain deviations bounded in $L_2$-norm, external disturbances for non-autonomous continuous Lipschitz systems. Here the gain of the observers depend on the time and are defined based on a numerical solution of optimization problems with differential linear matrix inequalities or numerical solution of the corresponding matrix comparison system. With the example of a single-link manipulator we show that their application for the state estimating of autonomous systems proves to be more efficient (in terms of convergence time and accuracy of the resulting estimates) as compared to observers with constant coefficients obtained with numerical solutions of optimization problems with linear matrix inequalities.