Regional consensus in discrete-time multi-agent systems subject to time-varying delays and saturating actuators

Abstract

This paper deals with consensus in discrete-time multi-agent systems under directed networks subject to time-varying delays and input saturation. Because saturation might prevent multi-agent systems from attaining consensus, system analysis and controller design require the characterization of the allowed region for the initial conditions. The main contributions of this work are sufficient conditions for consensus analysis and design of distributed protocols for discrete-time systems. Moreover, the conditions lead to a procedure allowing an estimate of the region of attraction. Such a procedure considers the effect of current and delayed states separately, yielding broader estimates of the allowed region for initial conditions. The results follow from the transformation of the consensus problem into a stability problem, with the subsequent employment of the Lyapunov-Krasovskii theory. The conditions are formulated as convex optimization problems. Finally, the paper presents examples and comparisons with previous approaches to illustrate the validity of the proposed methods.

Keywords:

• Consensus
• linear matrix inequalities
• discrete-time
• multi-agent systems
• saturation
• time-delay

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We used the inequality $2{\mathit{a}}^{\mathrm{\prime }}\mathit{b}\le {\mathit{a}}^{\mathrm{\prime }}X\mathit{a}+{\mathit{b}}^{\mathrm{\prime }}{X}^{-1}\mathit{b}$, where $\mathit{a}$, $\mathit{b}\in {\mathbb{R}}^{m(n-1)}$ and $X>0\in {\mathbb{R}}^{m(n-1)\times m(n-1)}$.

Additional information

Funding

This work was in part supported by the INCT (National Institute of Science and Technology) project [grant CNPq (Brazilian National Research Council) 465755/2014-3] and FAPESP (São Paulo Research Foundation) [2014/50851-0]. This work was also supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) (Finance Code 88887.136349/2017-00) and CNPq [grant numbers 315258/2020-9, 429819/2018-8, 312034/2020-2, and 311208/2019-3].