Backstepping with multi-stage polar controllers for MIMO nonlinear systems

Multi-stage polar controllers are proposed for control of MIMO systems when the dimension of the system n, is much higher then the number of control inputs, m. The idea of forcing the trajectory to enter fast a stabilizing manifold utilizing the concept of a polar partition and the polar control are combined with the backstepping idea to achieve stability (and ultimately achieve regulation, tracking and other control goals) for systems with strict feedback structure. The result is the imbedded polar controller structure that has exhibited a number of appealing features: methodological design, off-the-shelf control units, free design parameters and good robustness to plant perturbations