Tracking reference inputs in control systems described by a class of nonlinear differential-algebraic equations

The authors consider the problem of designing a feedback control law in order to achieve tracking of reference inputs in control systems described by a class of nonlinear differential-algebraic equations. The approach is based on an extension of the extended linearization methodology to the class of nonlinear differential-algebraic equations studied. The procedure is reduced to the design of state feedback control laws which asymptotically stabilize a class of parametrized linear differential-algebraic equations. Using the stability theorem of M. Kelemen (1986) and the concept of state realizations for nonlinear differential-algebraic equations, it is shown that the control design guarantees, at least locally, that the tracking error is bounded by any given bound provided the reference inputs are sufficiently slowly varying