Feedback control of affine nonlinear singular control systems

This paper discusses feedback control problems for affine nonlinear singular systems. Namely, the problems of regularization (regular singular systems have for a particular initial state and input, a unique solution), non-interaction and exact linearization. First, an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced. This algorithm resembles the well-known constrained dynamics algorithm for affine nonlinear systems. For regularizable affine nonlinear singular systems, necessary and sufficient conditions for the solvability of the non-interacting control problem are derived. They are based on another algorithm producing a sequence of integers, the generalization of the well known notion of relative degree for usual affine nonlinear systems. Finally, the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed. An example is provided to illustrate the main results.