access icon free Necessary and sufficient conditions for containment control of heterogeneous linear multi-agent systems with fixed time delay

The containment problem of heterogeneous multi-agent systems with fixed time delay under directed network is considered for both continuous-time and discrete-time multi-agent systems. Leaders and followers have different dynamics, modelled by double-integrator and single-integrator, respectively. It is also assumed that all leaders are stationary. Unlike the current approach in the literature which utilises LMIs to derive sufficient condition for containment reaching, the authors employ Laplace transform/Z-transform and final value theorem to obtain the necessary and sufficient condition which guarantees the containment of follower agents in the presence of communication delays. This approach gives the exact maximum allowed time delay, which is larger than the bound obtained by previous approaches. This study also proposes a noble reduced-order dynamic method, by adding virtual agents, in order to use final value theorem for stability analysis in the presence of heterogeneity in the network. In the end, to illustrate the effectiveness of the theoretical results, simulation examples are provided.

Inspec keywords: Laplace transforms; multi-agent systems; linear systems; discrete time systems; stability; delays; multi-robot systems

Other keywords: current approach; directed network; different dynamics; communication delays; discrete-time multiagent systems; containment problem; double-integrator; exact maximum allowed time delay; necessary condition; single-integrator; sufficient condition; containment reaching; leaders; heterogeneous multiagent systems; fixed time delay; final value theorem; heterogeneity; heterogeneous linear multiagent systems; containment control; reduced-order dynamic method; virtual agents

Subjects: Discrete control systems; Stability in control theory; Combinatorial mathematics; Linear control systems; Control system analysis and synthesis methods; Algebra

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