Stability analysis of constrained control systems: An alternative approach

The purpose of the present paper is to study stability of constrained nonlinear control systems. Usually, this is done by reducing the constrained control system to an unconstrained control system with respect to the constrained manifold. Different from these approaches, an alternative is proposed here which allows to establish stability without an explicit knowledge of the constrained manifold and the reduced unconstrained control system. The main result is a simple stability theorem. Despite its simplicity, the theorem can be applied to a broad class of stability problems, for example, the stability analysis of unstructured nonlinear differential–algebraic equations of higher index and to LaSalle's invariance principle. Furthermore, the theorem allows a computationally efficient stability analysis of the class of constrained polynomial control systems using semidefinite programming and the sum of squares decomposition.