Controller design for a class of nonlinear systems with input saturation using convex optimization

In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed.