Robustness property of high-gain observers for closed-loop nonlinear systems: theoretical study and robotics control application

The robust stability problem for a wide class of closed-loop nonlinear syst ems is considered. A nonlinear feedback is assumed to be a function of cur rent state estimates obtained by a nonlinear high-gain observer. The proble m is solved in the presence of essential parametric uncertainties as well a s external perturbation noise (mixed uncertainties). A two riccati-equation approach is applied We demonstrate that the high-gain observer under consi deration provides sufficiently good state-space estimates which are bounded 'on average'. The same property is valid for the trajectories of the close d-loop nonlinear system. The observation error bound is derived and tur ns out to be a linear combination of a priori given uncertainties levels of ex ternal input and output perturbations. If no uncertainties are considered i n the given model description, this bound is zero and corresponds to the as ymptotic globally stability property for the observation error as well as f or the state-space trajectories. The simulations results, concerning a robo t manipulator, illustrate the effectiveness of the suggested technique.