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

Abstract

The robust stability problem for a wide class of closed-loop nonlinear systems is considered. A nonlinear feedback is assumed to be a function of current state estimates obtained by a nonlinear high-gain observer. The problem is solved in the presence of essential parametric uncertainties as well as external perturbation noise (mixed uncertainties). A two Riccati-equation approach is applied. We demonstrate that the highgain observer under consideration provides sufficiently good state-space estimates which are bounded 'on average'. The same property is valid for the trajectories of the closed-loop nonlinear system. The observation error bound is derived and turns out to be a linear combination of a priori given uncertainties levels of external input and output perturbations. If no uncertainties are considered in the given model description, this bound is zero and corresponds to the asymptotic globally stability property for the observation error as well as for the state-space trajectories. The simulations results, concerning a robot manipulator, illustrate the effectiveness of the suggested technique.