A Computationally Lyapunov Nonlinear Gain Scheduling Control of Nonlinear Systems with Stability Guarantees

The present work proposes an advanced gain scheduling controller synthesis approach which is based on the methodological theory of Lyapunov design. We exploit an original procedure to enlarge the domain of attraction of a nonlinear affine system based on the Zubov Theorem. Then we construct control Lyapunov functions to various operating points of the studied process. A Lyapunov-based control synthesis algorithm is used to construct a control law that guarantees stability and high precision along the desired trajectory. We demonstrate the performances of the control design procedure on a second order nonlinear chemical reactor CSTR model characterized by multiple operating points. A simulation study is developed to show the efficiency of the proposed method.