On practical input to state stabilization for nonlinear discrete-time systems: A dynamic programming approach

A novel technique for synthesizing dynamic state feedback controllers that achieve practical input to state stability (PISS) property for nonlinear discrete-time systems is presented. The PISS controller design for the original system is solved via an auxiliary l
^∞
-bounded (LIB) robustness synthesis problem for an auxiliary system. A complete solution for the LIB synthesis problem has been presented recently in the literature. The obtained static state feedback LIB controller for the auxiliary system can be interpreted as a dynamic state feedback PISS controller for the original system. The obtained solution is in terms of a dynamic programming equation (or inequality).