Leonov Redesign: A Robustification Method for Multistable Systems with State-Periodic Dynamics

In this paper, the Lyapunov redesign technique is revisited for a class of state-periodic systems. The proposed robustification method is based on the novel Leonov function approach that offers relaxed conditions for establishing global boundedness of solutions of state-periodic systems compared with using Lyapunov functions. Then, assuming that the system under study achieves a desired behavior described by a known Leonov function in the absence of perturbations, our main result provides a robustifying controller that preserves this desired behavior in the presence of matched bounded perturbations. The proposed approach is applied to enhance the robustness of a microgrid with a mixed rotational and inverter-interfaced generation pool. Numerical simulations show the effectiveness of this technique.