Feedback stabilization of control systems described by a class of nonlinear differential-algebraic equations

Abstract

A theoretical framework for the stabilization of control systems defined by a class of nonlinear differential-algebraic equations is established. Assumptions are stated which guarantee that the nonlinear differential-algebaric equations can be described by a nonlinear control system defined on a smooth manifold. A procedure for obtaining a local state realization is developed. Conditions for local stabilization of a single equilibrium solution, including one set of conditions which can easily be checked using standard computations, are indicated.