Gramian-Based Characterization of Network Vulnerability to Nodal Impulse Inputs: Preprint

Prasad Chanekar, Bala Kameshwar Poolla, Jorge Cortes

Research output: Contribution to conferencePaper


Impulsive inputs applied at influential nodes of a network system may result in undesirable behavior and degrade performance. This paper proposes the notion of vulnerability matrix (VM) to characterize the effect of impulse inputs on a network following either discrete-time or continuous-time dynamics. The VM describes the first-order effects of impulse inputs on edge flows and is based on the controllability Gramian. We provide explicit expressions for the elements of the vulnerability matrix for the class of directed line networks in terms of the edge weights. Simulations validate our results and highlight the utility of the proposed metric in capturing the transient effects of nodal impulse inputs on edge flows.
Original languageAmerican English
Number of pages9
StatePublished - 2023
Event2023 American Control Conference (ACC) - San Diego, California
Duration: 31 May 20232 Jun 2023


Conference2023 American Control Conference (ACC)
CitySan Diego, California

NREL Publication Number

  • NREL/CP-5D00-84135


  • controllability Gramian
  • directed line networks
  • network systems


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