Handling disturbances in nonlinear control: the use of state feedback

The problem of controlling a nonlinear system in the presence of disturbances and modelling inaccuracies is considered. The objective is to design a static state feedback controller that controls the system so that the combined effect of all disturbances and inaccuracies on the response of the closed loop system is below a specified bound. The results include a characterization of the largest disturbance amplitude for which the design objective can be met. This result can be used to find the largest discretization step for a digital controller. Note that a larger discretization step lowers the computational burden of the controller. By exploring a basic connection to reachability, a procedure for the computation of appropriate static state feedback controllers is described. The state feedback controllers are calculated through the solution of a system of algebraic inequalities.