Passivity-based Decentralized Control for Discrete-time Large-scale Systems

TL;DR

This paper introduces a novel decentralized control method for large-scale discrete-time systems that guarantees passivity directly, ensuring stability without relying on continuous-time passivity properties, and is validated on DC microgrids.

Contribution

It proposes a new passivity-based decentralized control scheme for discrete-time systems that avoids passivity loss during discretization and ensures system stability.

Findings

Controller guarantees passivity in discrete-time systems.

Ensures asymptotic stability through local passivity conditions.

Validated effectiveness on a DC microgrid case study.

Abstract

Passivity theory has recently contributed to developing decentralized control schemes for large-scale systems. Many decentralized passivity-based control schemes are designed in continuous-time. It is well-known, however, that the passivity properties of continuous-time systems may be lost under discretization. In this work, we present a novel stabilizing decentralized control scheme by ensuring passivity for discrete-time systems directly and thus avoiding the issue of passivity preservation. The controller is synthesized by locally solving a semidefinite program offline for each subsystem in a decentralized fashion. This program comprises local conditions ensuring that the corresponding subsystem is locally passive. Passivity is ensured with respect to a local virtual output which is different from the local actual output. The program also comprises local conditions ensuring that the local passivity of all subsystems implies the asymptotic stability of the whole system. The performance of the proposed controller is evaluated on a case study in DC microgrids.