Abstract
In recent years the main focus of research in the area of robust stability of systems was on linear systems. In this paper the question of robust stability for nonlinear systems is adressed. We are mainly interested in global asymptotic stability and the main tools to solve these problems are methods based on Lyapunov functions. Using an appropriate Lyapunov function and an exact linearization of the system we are able to derive a sufficient condition for global asymptotic stability of a nonlinear system. This sufficient condition is known in the literature as robust linear matrix inequality. The main contribution of this paper is a new relaxation for robust linear matrix inequalities which avoids vertexization and leads to a computationally efficient procedure.
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