Topics

Passivity and Nonlinear Control

Passivity is an energy-based property that is especially useful for interconnected and nonlinear systems. Because passive systems preserve stability under broad classes of interconnections, passivity provides a constructive way to move between component-level properties and network-level guarantees.

Our work uses passivity both as an analysis tool and as a synthesis tool. A recurring theme is the connection between passivity, monotonicity, convex network optimization, cooperative control of systems that are not passive before feedback design, and newer geometric notions of dissipativity relative to target manifolds.

Passivity, Duality, and Network Optimization

Passivity-based cooperative control can be interpreted through the lens of network optimization. This viewpoint reveals a duality between diffusive interconnections and optimization constraints, and it explains why steady-state behavior in passive networks often solves an implicit optimization problem.

These results connect edge agreement, passivity analysis, inverse optimality, and distributed controller synthesis for networked systems.

Duality between diffusive networks and network optimization
Duality between diffusive network interconnections and optimization structure.

Representative Publications:

  1. M. Sharf and D. Zelazo, “Analysis and Synthesis of MIMO Multi-Agent Systems Using Network Optimization,” IEEE Transactions on Automatic Control, 64(11):1558–2523, 2019.
    Sharf2017b_J.pdf DOI: 10.1109/tac.2019.2908258 Sharf2017b_J.bibtex
  2. M. Sharf and D. Zelazo, “A Network Optimization Approach to Cooperative Control Synthesis,” IEEE Control Systems Letters, 1(1):86–91, 2017.
    Sharf2017a_J.pdf DOI: 10.1109/lcsys.2017.2706948 Sharf2017a_J.bibtex
  3. M. Bürger, D. Zelazo, and F. Allgöwer, “Duality and network theory in passivity-based cooperative control,” Automatica, 50(8):2051–2061, 2014.
    Burger2014_J.pdf DOI: 10.1016/j.automatica.2014.06.002 Burger2014_J.bibtex
  4. M. Bürger, D. Zelazo, and F. Allgöwer, “On the Steady-State Inverse-Optimality of Passivity-Based Cooperative Control,” in 4th IFAC Workshop on Distributed Estimation and Control in Networked System, Koblenz, Germany, Sep. 2013.
    Mathias2013.pdf DOI: 10.3182/20130925-2-DE-4044.00004 Mathias2013.bibtex
  5. D. Zelazo and M. Mesbahi, “Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis,” IEEE Transactions on Automatic Control, 56(3):544–555, 2011.
    Zelazo2009b_J.pdf DOI: 10.1109/TAC.2010.2056730 Zelazo2009b_J.bibtex

Passivation of Passive-Short Systems

Many nonlinear systems are not passive with the inputs and outputs available to the controller. Passivation asks how to transform or regularize the input-output map so that the resulting closed-loop component can be safely interconnected with other agents.

Our work develops geometric and optimization-based passivation methods for passive-short systems, including characterizations of passivizing input-output transformations for SISO and MIMO nonlinear systems.

Passivation through monotonicity and convexity
Passivation through geometric, monotonicity, and convexity-based transformations.

Representative Publications:

  1. M. Sharf and D. Zelazo, “A Characterization of Passivizing Input-Output Transformations of Nonlinear MIMO Systems,” IEEE Control Systems Letters, 8:2733–2738, 2024.
    Sharf2024_J.pdf DOI: 10.1109/LCSYS.2024.3513238 Sharf2024_J.bibtex
  2. M. Sharf and D. Zelazo, “A Characterization of All Linear Passivizing Input-Output Transformations of a Passive-Short System: The SISO Case,” IEEE Control Systems Letters, 8:532–537, 2024.
    Sharf2021c_J.pdf Sharf2021c_J.slides DOI: 10.1109/LCSYS.2024.3396616 Sharf2021c_J.bibtex
  3. M. Sharf, A. Jain, and D. Zelazo, “Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passive-Short Systems,” IEEE Transactions on Automatic Control, 66(12):5877–5892, 2021.
    Sharf2019c_J.pdf DOI: 10.1109/tac.2020.3043390 Sharf2019c_J.bibtex
  4. M. Sharf, “Network Optimization Methods in Passivity-Based Cooperative Control,” phdthesis, Technion - Israel Institute of Technology, Aerospace Engineering Department, 2020.
    Sharf2020.pdf Sharf2020.bibtex
  5. M. Sharf and D. Zelazo, “Network Feedback Passivation of Passivity-Short Multi-Agent Systems,” IEEE Control Systems Letters, 3(3):607–612, 2019.
    Sharf2019a_J.pdf Sharf2019a_J.slides DOI: 10.1109/lcsys.2019.2914128 Sharf2019a_J.bibtex
  6. A. Jain, M. Sharf, and D. Zelazo, “Regularization and Feedback Passivation in Cooperative Control of Passivity-Short Systems: A Network Optimization Perspective,” IEEE Control Systems Letters, 2(4):731–736, 2018.
    Jain2018a_J.pdf DOI: 10.1109/lcsys.2018.2847738 Jain2018a_J.bibtex

Transversal and Geometric Passivity

Classical passivity usually measures energy exchange relative to an equilibrium, a shifted equilibrium, or a pair of trajectories. Transversal passivity changes the reference object: the target can be a manifold, orbit, agreement set, or other geometric constraint, and the dissipation certificate only penalizes motion transverse to that target.

Our ongoing work develops this geometric viewpoint for interconnected systems. The central objects are manifold error maps, tubular retractions, and compatibility conditions that allow feedback interconnections to preserve transverse dissipativity. This gives a passivity framework for behaviors such as agreement, synchronization, and limit-cycle regulation, where motion along the target set should remain free.

Manifold error map for transversal passivity
Geometric passivity uses manifold error maps to measure the transverse distance to a target set.

Related Material:

Toward a Geometric Theory of Passivity presents the current transversal passivity framework.

Nonlinear Consensus and Identification

Passivity also gives tools for analyzing nonlinear consensus, orientation effects in directed networks, and data-driven questions such as network identification. In these problems, the passivity property acts as a bridge between local nonlinear dynamics and global graph-dependent behavior.

This direction connects passivity analysis on digraphs, network feedback passivation, and passivity-based methods for recovering network structure.

Network feedback passivation architecture
Network feedback passivation for cooperative control of passive-short agents.

Representative Publications:

  1. F. Yue and D. Zelazo, “A Passivity Analysis for Nonlinear Consensus on Digraphs,” in 64th IEEE Conference on Decision and Control, Rio de Janerio, Brazil, Dec. 2025.
    Yue2025_CDC.pdf Yue2025_CDC.slides Yue2025_CDC.bibtex
  2. M. Sharf and D. Zelazo, “Symmetry-Induced Clustering in Multi-Agent Systems using Network Optimization and Passivity,” in 27th Mediterranean Conference on Control and Automation, Akko, Israel, Jul. 2019.
    Sharf2019a.pdf Sharf2019a.slides DOI: 10.1109/med.2019.8798507 Sharf2019a.bibtex
  3. M. Sharf and D. Zelazo, “Network Feedback Passivation of Passivity-Short Multi-Agent Systems,” IEEE Control Systems Letters, 3(3):607–612, 2019.
    Sharf2019a_J.pdf Sharf2019a_J.slides DOI: 10.1109/lcsys.2019.2914128 Sharf2019a_J.bibtex
  4. M. Sharf and D. Zelazo, “Network Identification: A Passivity and Network Optimization Approach,” in IEEE Conference on Decision and Control, Miami, Florida, Dec. 2018.
    Sharf2018a.pdf DOI: 10.1109/cdc.2018.8619059 Sharf2018a.bibtex

Related Publications:

  1. F. Yue and D. Zelazo, “A Passivity Analysis for Nonlinear Consensus on Digraphs,” in 64th IEEE Conference on Decision and Control, Rio de Janerio, Brazil, Dec. 2025.
    Yue2025_CDC.pdf Yue2025_CDC.slides Yue2025_CDC.bibtex
  2. M. Sharf and D. Zelazo, “A Characterization of Passivizing Input-Output Transformations of Nonlinear MIMO Systems,” IEEE Control Systems Letters, 8:2733–2738, 2024.
    Sharf2024_J.pdf DOI: 10.1109/LCSYS.2024.3513238 Sharf2024_J.bibtex
  3. M. Sharf and D. Zelazo, “A Characterization of All Linear Passivizing Input-Output Transformations of a Passive-Short System: The SISO Case,” IEEE Control Systems Letters, 8:532–537, 2024.
    Sharf2021c_J.pdf Sharf2021c_J.slides DOI: 10.1109/LCSYS.2024.3396616 Sharf2021c_J.bibtex
  4. M. Sharf, A. Jain, and D. Zelazo, “Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passive-Short Systems,” IEEE Transactions on Automatic Control, 66(12):5877–5892, 2021.
    Sharf2019c_J.pdf DOI: 10.1109/tac.2020.3043390 Sharf2019c_J.bibtex
  5. M. Sharf, “Network Optimization Methods in Passivity-Based Cooperative Control,” phdthesis, Technion - Israel Institute of Technology, Aerospace Engineering Department, 2020.
    Sharf2020.pdf Sharf2020.bibtex
  6. M. Sharf and D. Zelazo, “Analysis and Synthesis of MIMO Multi-Agent Systems Using Network Optimization,” IEEE Transactions on Automatic Control, 64(11):1558–2523, 2019.
    Sharf2017b_J.pdf DOI: 10.1109/tac.2019.2908258 Sharf2017b_J.bibtex
  7. M. Sharf and D. Zelazo, “Symmetry-Induced Clustering in Multi-Agent Systems using Network Optimization and Passivity,” in 27th Mediterranean Conference on Control and Automation, Akko, Israel, Jul. 2019.
    Sharf2019a.pdf Sharf2019a.slides DOI: 10.1109/med.2019.8798507 Sharf2019a.bibtex
  8. M. Sharf and D. Zelazo, “Network Feedback Passivation of Passivity-Short Multi-Agent Systems,” IEEE Control Systems Letters, 3(3):607–612, 2019.
    Sharf2019a_J.pdf Sharf2019a_J.slides DOI: 10.1109/lcsys.2019.2914128 Sharf2019a_J.bibtex
  9. M. Sharf and D. Zelazo, “Network Identification: A Passivity and Network Optimization Approach,” in IEEE Conference on Decision and Control, Miami, Florida, Dec. 2018.
    Sharf2018a.pdf DOI: 10.1109/cdc.2018.8619059 Sharf2018a.bibtex
  10. A. Jain, M. Sharf, and D. Zelazo, “Regularization and Feedback Passivation in Cooperative Control of Passivity-Short Systems: A Network Optimization Perspective,” IEEE Control Systems Letters, 2(4):731–736, 2018.
    Jain2018a_J.pdf DOI: 10.1109/lcsys.2018.2847738 Jain2018a_J.bibtex
  11. M. Sharf and D. Zelazo, “A Network Optimization Approach to Cooperative Control Synthesis,” IEEE Control Systems Letters, 1(1):86–91, 2017.
    Sharf2017a_J.pdf DOI: 10.1109/lcsys.2017.2706948 Sharf2017a_J.bibtex
  12. M. Bürger, D. Zelazo, and F. Allgöwer, “Duality and network theory in passivity-based cooperative control,” Automatica, 50(8):2051–2061, 2014.
    Burger2014_J.pdf DOI: 10.1016/j.automatica.2014.06.002 Burger2014_J.bibtex
  13. M. Bürger, D. Zelazo, and F. Allgöwer, “On the Steady-State Inverse-Optimality of Passivity-Based Cooperative Control,” in 4th IFAC Workshop on Distributed Estimation and Control in Networked System, Koblenz, Germany, Sep. 2013.
    Mathias2013.pdf DOI: 10.3182/20130925-2-DE-4044.00004 Mathias2013.bibtex
  14. D. Zelazo and M. Mesbahi, “Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis,” IEEE Transactions on Automatic Control, 56(3):544–555, 2011.
    Zelazo2009b_J.pdf DOI: 10.1109/TAC.2010.2056730 Zelazo2009b_J.bibtex