Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this paper, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities are developed. Issues concerning proper initialization and simulation are also considered. Illustrative examples are provided.