Stochastic Semistability for Nonlinear Dynamical Systems with Application to Consensus on Networks with Communication Uncertainty

Wassim M. Haddad, Tanmay Rajpurohit, Xu Jin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This article focuses on semistability and finite time semistability analysis and synthesis of stochastic dynamical systems having a continuum of equilibria. Stochastic semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to Lyapunov stable in probability equilibrium points determined by the system initial conditions. In this article, we extend the theories of semistability and finite-time semistability for deterministic dynamical systems to develop a rigorous framework for stochastic semistability and stochastic finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for stochastic semistability are developed for dynamical systems driven by Markov diffusion processes. These results are then used to develop a general framework for designing semistable consensus protocols for dynamical networks in the face of stochastic communication uncertainty for achieving multiagent coordination tasks in finite time. The proposed controller architectures involve the exchange of generalized charge or energy state information between agents guaranteeing that the closed-loop dynamical network is stochastically semistable to an equipartitioned equilibrium representing a state of almost sure consensus consistent with basic thermodynamic principles.

Original languageEnglish
Article number8793118
Pages (from-to)2826-2841
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 2020

Bibliographical note

Funding Information:
Manuscript received March 11, 2019; revised June 5, 2019; accepted July 29, 2019. Date of publication August 9, 2019; date of current version June 27, 2020. This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-16-1-0100. Recommended by Associate Editor M. Cao. (Corresponding author: Wassim M. Haddad.) W. M. Haddad and X. Jin are with the School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:,;

Publisher Copyright:
© 1963-2012 IEEE.


  • Communication uncertainty
  • Markov processes
  • consensus protocols
  • distributed control
  • nonlinear networks
  • stochastic finite time semistability
  • stochastic semistability
  • thermodynamic protocols

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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