Krasovskii Passivity for Sampled-Data Stabilization and Output Consensus

In this paper, we establish the novel concept of Krasovskii passivity for sampled discrete-time nonlinear systems, utilizing Krasovskii passivity for control design under sampling. We consider two separate control objectives: stabilization and output consensus, where the latter is studied under the presence of an unknown constant disturbance. Drawing inspiration from established methodologies in the continuous-time domain, we design sampled-data control schemes for each control objective, leveraging Krasovskii passivity. The proposed sampled discrete-time controllers are respectively validated through simulations on a DC microgrid of boost converters and a DC microgrid of buck converters whose continuous-time models and their implicit midpoint discretizations are Krasovskii passive in each time scale.