access icon free Distributed sampled-data containment control of linear multi-agent systems with fixed topology

© The Institution of Engineering and Technology
Received 28/11/2016, Accepted 23/05/2017, Revised 12/05/2017, Published 26/05/2017

This study investigates the sampled-data containment control problem for linear multi-agent systems with multiple leaders under undirected or directed network topology. First, by means of the decomposition method, the containment control problem is transformed into the simultaneous stability analysis issue of certain subsystems. Then, the solution of a class of differential equations, which plays a key role for the addressed problem, is exploited by using the contradiction method. Together with a novel Lyapunov function, sufficient conditions are established to guarantee that all the followers move into the convex hull spanned by the leaders. The proposed results are dependent on the information of the system dynamics, the coupling strength as well as the eigenvalues of topology matrix. Furthermore, the established results are specialised to both the leader–following case and the traditional consensus case. Finally, simulations are given to illustrate the theoretical results derived in this study.

Inspec keywords: differential equations; directed graphs; distributed control; set theory; network theory (graphs); eigenvalues and eigenfunctions; matrix decomposition; linear systems; stability; Lyapunov methods; sampled data systems

Other keywords: multiple leaders; Lyapunov function; sufficient conditions; convex hull; system dynamics; leader-following system; directed network topology; distributed sampled-data containment control problem; topology matrix eigenvalues; coupling strength; simultaneous stability analysis; differential equations; undirected network topology; fixed topology; linear multiagent systems; decomposition method; contradiction method

Subjects: Differential equations (numerical analysis); Stability in control theory; Multivariable control systems; Combinatorial mathematics; Discrete control systems; Linear control systems; Linear algebra (numerical analysis)

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