Networked Negative Imaginary Systems

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1. Motivation: From Single Systems to Networks

Many modern engineering systems are not isolated, but consist of multiple dynamical subsystems interacting over a network.

Examples include:

  • groups of robots coordinating motion,
  • power generators interacting through transmission networks,
  • flexible structures coupled via mechanical or electrical links.

While the negative imaginary (NI) property provides powerful stability guarantees for single systems, interconnecting multiple NI systems introduces new challenges:

  • communication may be local rather than centralized,
  • network topology directly affects stability and performance,
  • systems in the network might have heterogeneous dynamics.

How to achieve stability for a network of nonlinear NI systems?

2. Networked NI Systems: Core Idea

Consider a collection of subsystems that are NI.

In a networked setting:

  • the input to each agent depends on relative outputs of its neighbors,
  • the interconnection is typically described by a graph Laplacian or incidence matrix,
  • feedback is distributed and does not rely on global information.

A key observation underlying my work is:

NI property still exists in the augmented system describing all the subsystems connected according to the graph topology.

3. Consensus

One important class of problems in multi-agent systems is consensus, where agents aim to agree on a common output or trajectory.

4. My Contributions

I established a control framework for the output feedback consensus for nonlinear NI systems under both:

  • identical agent dynamics,
  • heterogeneous agent dynamics.

These results extend classical consensus theory beyond passive systems and linear NI systems, and apply to systems with free body motion.

  1. Robust Output Feedback Consensus for Networked Identical Nonlinear Negative-Imaginary Systems (MTNS 2020)

  2. Robust Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems (ANZCC 2020)

  3. Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems With Free-Body Motion (IEEE TAC 2023)

5. Applications

The results in the articles listed above have been further extended for applications in power systems control. For more details, explore the topic .