LPV Scheme for Robust Adaptive Output Feedback Consensus of Lipschitz Multiagents Using Lipschitz Nonlinear Protocol

Ateeq Ur Rehman, Muhammad Rehan, Naeem Iqbal, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


This article addresses the robust nonlinear adaptive consensus protocol design approach, for nonlinear multiagent (MA) systems under external perturbations with Lipschitz dynamics. Based on the existing results of the adaptive protocol using relative output information, a modified robust nonlinear adaptive consensus protocol for MAs is proposed. The Lipschitz nonlinearity in the agents' dynamics and the adaptive protocol are reformulated using a composite linear parameter-varying (LPV) approach. Our composite LPV reformulation is less restrictive because it utilizes all the properties of Lipschitz functions. Consensus protocol design conditions based on the proposed reformulation of Lipschitz nonlinearities, Lyapunov theory, and the modified nonlinear consensus protocol are derived to attain the exponential consensus. The proposed consensus protocol approach is further extended by providing necessary and sufficient conditions for the straightforward evaluation of the robust adaptive protocol gains. The proposed fully distributed consensus protocol is robust to ensure the consensus error and adaptive gains bounded by eliminating the effect of disturbances. The resultant consensus control scheme reduces conservatism and is feasible for large values of Lipschitz constants. Finally, simulation results are presented for verifying the potency of the developed control strategies.

Original languageEnglish
Pages (from-to)7040-7050
Number of pages11
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number11
Publication statusPublished - 2021 Nov 1

Bibliographical note

Funding Information:
This work was supported in part by HEC of Pakistan under National Centre in Cyber Security projects Critical Infrastructure Protection and Malware Analysis Lab at PIEAS, and in part by the National Research Foundation of Korea through the Ministry of Science, ICT and Future Planning under Grant NRF-2017R1A1A1A05001325. The work of Ateeq ur Rehman was supported by the Higher Education Commission (HEC) of Pakistan through Ph.D. Scholarship under phase II batch III indigenous scholarship program.

Publisher Copyright:
© 2013 IEEE.


  • Composite linear parameter-varying (LPV) reformulation
  • Lipschitz nonlinearity
  • consensus
  • disturbance
  • multiagents (MAs)
  • robust adaptive consensus

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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