Among different distributed network localisation methods, displacement‐based network localisation with orientation estimation is an effective approach because it does not require global information and yet asymptotically produces accurate estimates. In this paper, to improve transient performance of this approach, non‐linear laws to achieve fixed‐time orientation estimation and fixed‐time displacement‐based localisation are proposed. A sequential algorithm ensuring fixed‐time convergence property and show uniform asymptotic stability of a fixed‐time network localisation with simultaneous fixed‐time orientation estimation is further provided. Simulation results verify that the proposed laws achieve network localisation of multi‐agent systems within fixed settling time.

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This paper addresses the consensus control problem in multi‐agent systems under the influence of diffusively coupled disturbances. Two different types of systems are considered regarding the homogeneity of the disturbance coupling parameters. The main goal is to derive conditions that guarantee the prescribed performance of the designed control system on disturbance attenuation. To estimate the disturbance attenuation performance of the controller, the ℋ∞$$ {\mathscr{H}}_{\infty } $$ norm of the transfer function from the redefined disturbance vector to the disagreement vector is measured. Then the sufficient conditions for the system to achieve consensus within the desired performance are derived in terms of linear matrix inequalities (LMI). Numerical examples of both one‐ and multi‐dimensional consensus control systems are provided to check the validity of the derived LMI feasibility test along with the illustration of consensus behavior in time domain.

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