Model predictive control of linear continuous time singular systems subject to input constraints

In this note we consider the stabilization of linear continuous time singular systems with respect to input constraints. Specifically we propose the use of a sampled-data model predictive control scheme. Stability of the closed-loop is achieved in a similar manner as for nonsingular systems, utilizing a suitable terminal penalty term and a terminal region constraint. One problem that must be overcome is the avoidance of impulsive solutions. This is achieved by enforcing the input to be sufficiently often differentiable. As shown, the resulting sampled-data model predictive control scheme does lead to stability in the sense of convergence and to an impulse free closed-loop.