109 Robust Stabilizing Controllers for Nonlinear Systems That Have an Undesirable Equilibrium Point Using an Approximate Linearization

In this paper, we examine a design method for robust stabilizing controllers for nonlinear systems that have an undesirable equilibrium point losing approximate feedback linearization. We adopt a three-step procedure to solve this problem. First, a state transformation matrix is determined, so that the nominal nonlinear system, of which that the equilibrium point is changed, is transformed approximately into the controllable canonical form. Then, the nonlinear system is divided into the controllable canonical representation section and the remainder. Second, the standard nonlinear feedback linearization method is used to transform the controllable canonical form into linear systems. Third, using quadratic stabilizing method, we can design robust stabilizing controllers.