Realization of high index differential-algebraic systems using singularly perturbed sliding manifolds

One of the key difficulties in control of nonlinear differential-algebraic equation (DAE) systems is that they are not expressed in an explicit state space form required by most design methods. To address this problem methods have been proposed to formulate state space approximations of DAEs. This process, known as realization, has been successful only for limited classes of problems. In this paper, a new approach is developed for constructing state space approximations for a general class of nonlinear high index DAEs. This is achieved by establishing new connections between DAE systems and control theory that result in a new type of nonlinear control problem. Boundary layer sliding control is combined with elements of singular perturbation theory to develop an efficient approximation with guaranteed error bounds. This leads to the singularly perturbed sliding manifold approach for DAE realization.