Nonlinear control using homotopy methods

Homotopy and continuation methods are commonly used tools in numerical analysis to solve nonlinear algebraic equations and optimisation problems. In this paper they are used to generalise the feedback controller design based on the well-known linearisation around an operating point. The result is a nonlinear feedback control law with guaranteed closed loop stability properties. The advantages are very unrestrictive conditions on the plant to be controlled and the possibility to upgrade a reliable linear controller.