On Control System Described by a Class of Nonlinear Differential-Algebraic Equations: State Realization and Local Control

A theoretical framework for the study of control systems defined by a class of nonlinear differential-algebraic equations is established. We first introduce the class of nonlinear control system considered, which is represented by a special but important class of nonlinear differential-algebraic equations. Assumptions are given for which the defining nonlinear differential-algebraic equations are well posed, in the sense that for given input and given consistent initial data, in a specified smooth manifold, there exists a unique smooth solution. A procedure for obtaining a local nonlinear state realization is developed; this realization can thus form the basis for control of the original differential-algebraic system. An approach for design of a linear feedback controller which achieves local regulation near an equilibrium solution is suggested. The framework established in this paper generalizes recent developments for control of mechanical systems with holonomic constraints and for control of mechanical systems with classical nonholonomic constraints.