Stabilization of Nonlinear Systems with Non-Polynomial Nonlinearities using SOS-Programming

M. Bäuml and J. Deutscher (Germany)


nonlinear control, Lyapunov stability, SOS-programming


This paper presents a numerical approach for the design of a nonlinear control law for nonlinear systems by extending the results for controller design using SOS-programming (see e.g. [1]) to non-polynomial systems. A polynomial approximation of the non-polynomialsystem with an upper bound of the approximation error on a predefined interval is determined. This upper bound is used in the SOS-program to determine a stabilizing control law and a Lyapunov function. The aim of the design method is to maximize the estimation of the region of attraction of the equilibrium of the closed loop non-polynomial system. An academic example demonstrates the presented approach.

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