This paper contributes to the solution of mobile robots rendezvous problem via the negative imaginary (NI) systems theory. Cooperative control strategies are proposed for integrator NI systems. These control strategies are beneficial because they can be directly applied to wheeled mobile robots. First, we show that the NI property is preserved for multiple multi-input multi-output (MIMO) integrator systems with directional information flow that is balanced and strongly connected. Then, we derive conditions that guarantee output consensus and output tracking for strongly connected, balanced and directed networks of integrators subject to energy-bounded disturbances using the NI internal stability theorems. Finally, experimental and simulation results are provided to validate the effectiveness of the proposed NI cooperative tracking results to achieve rendezvous of multiple nonholonomic wheeled mobile robots.

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Summary This paper deals with the distributed robust stabilization problem for networked multiagent systems with strict negative imaginary (SNI) uncertainties. Communication among agents in the network is modelled by an undirected graph with at least one self‐loop. A protocol based on relative state measurements of neighbouring agents and absolute state measurements of a subset of agents is considered. This paper shows how to design the protocol parameters such that the uncertain closed‐loop networked multiagent system is robustly stable against any SNI uncertainty within a certain set for various different network topologies. Tools from negative imaginary (NI) theory are used as an aid to simplify the problem and synthesise the protocol parameters. We show that a state, input, and output transformation preserves the NI property of the network. Consequently, a necessary and sufficient condition for the transfer function matrix of the nominal closed‐loop networked system to be NI and satisfy a DC gain condition is that multiple reduced‐order equivalent systems be NI and satisfy a DC gain condition simultaneously. Based on the reduced‐order systems, we derive sufficient conditions in an LMI framework which ensure the existence of a protocol satisfying the desired objectives. A numerical example is given to confirm the effectivenesses of the proposed results.

This paper is concerned with robust output consensus for networks of homogeneous negative imaginary (NI) systems under L2 external disturbances and model uncertainty in a generalised framework. By removing certain assumptions which had been imposed in earlier studies, we derive generalised conditions that guarantee robust output consensus of the networked systems by means of recently published generalised internal stability results for NI systems. The proposed conditions are shown to reduce to earlier conditions in literature by imposing the same assumptions. A convergence analysis is also provided which is in agreement with the conclusions of previous literature. An example that demonstrates the effectiveness of the results is also provided.

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