## Robustification and Parametrization of Switching Controllers for a Class of Set Invariance Problems
In this paper, we consider the robustification and parametrization of an invariance switching controller with respect to a scalar variable (parameter) that affects the system dynamics. By robustification, we mean searching for a switching controller that guarantees invariance of a set, under a large enough range of the parameter values. In case such a robust controller does not exist, we do parametrization, i.e., searching for a collection of controllers, each one robust to a smaller range of parameter values. A parametrized controller can be applied in real-time by picking the appropriate switching surfaces based on the measurement of the parameter. To be more specific, assuming (i) the system dynamics is affine, and is monotone in the considered parameter, (ii) the invariance switching controller is defined on a rectangle in the state space, we show that the robustification and parametrization problems can be reduced to solving a sequence of linear programming problems. The proposed approach is illustrated by several numerical examples. |