Control of linear systems with affine constraints: a gain-scheduling approach

A gain scheduling based on a one-parameter family of Lyapunov functions is presented for the control of linear systems with affine constraints. The tuning of the parameter in the control law is assumed to result from a trade-off between the size of the state-space domain where the constraints are satisfied and the closed-loop performance. A target controller is chosen for local performance in this family. The proposed online scheduling is aimed at reaching the target controller in the fastest possible way, while guaranteeing satisfaction of the constraints along closed-loop solutions.