Nonlinear System Controller Design based on Domain of Attraction

A technique for analyzing and designing controllers for nonlinear systems based on measures of the domain of attraction is presented. The domain of attraction is the region of initial conditions that tend toward an attractor. A refinement of this region is the domain of performance which is the region of initial conditions that meet a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region, hence, the domain indicates the ability of a nonlinear system to recover from state perturbations. This global design technique is contrasted with more traditional, local design methods. Design examples of both linear and nonlinear controllers are shown for an inverted pendulum.