Asymptotic and Finite-Time Semistability for Nonlinear Discrete-Time Systems With Application to Network Consensus

• 成果类型: Article
• 署名作者: Haddad, Wassim M.; Lee, Junsoo; Bhat, Sanjay P.
• 署名单位: University System of Georgia; Georgia Institute of Technology; Tata Sons; Tata Consultancy Services Limited (TCS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3142189
• 发表日期: 2023
• 页码: 766-781
• 关键词: Consensus control; Discrete systems; finite-time semistability; Lyapunov theorems; nonlinear networks; semistability; thermodynamic protocols

摘要

This article focuses on semistability and finite-time semistability analysis and synthesis of discrete-time dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this article, we build on the theories of semistability and finite-time semistability for continuous-time dynamical systems to develop a rigorous framework for discrete semistability and discrete finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for semistability and finite-time semistability are developed, and the regularity properties of the Lyapunov function establishing finite-time semistability are shown to be related to the settling time function capturing the finite settling time behavior of the dynamical system. These results are then used to develop a general framework for designing semistable and finite-time semistable consensus protocols for discrete dynamical networks for achieving multiagent coordination tasks asymptotically and in finite time. The proposed controller architectures involve the exchange of generalized energy state information between agents guaranteeing that the closed-loop dynamical network is semistable to an equipartitioned equilibrium representing a state of consensus consistent with basic thermodynamic principles.