Controller design for systems with state constraints

For nonlinear systems affine in the control, controller design is considered with constraints on state variables. A change of variables is proposed to establish the diffeomorphism between the constrained domain in the original coordinates and the whole state space in the new coordinates. The introduction of the diffeomorphism eliminates the constraints on state variables for the transformed systems, and attention can simply be focused on the global controller design of the transformed systems. The proposed general theory is applied to two special cases for which respective applications are given.