Performance Preserving Integral Extension of Linear and Homogeneous State-Feedback Controllers

The problem of extending an existing state-feedback controller by an integrator is considered. A structural insight into the design of such controllers is presented for the linear case, which allows to preserve the performance of the given controller in a certain sense. Using this insight, a second order homogeneous state feedback controller with discontinuous integral action is proposed, which can reject arbitrary slope bounded, i.e., Lipschitz continuous, perturbations. By means of Lyapunov methods, stability conditions for the closed loop system and a bound for its finite convergence time are derived. Numerical simulations illustrate the results and provide further insight into the tuning of the proposed approach.