Any cooperative control scheme relies on some measurements which are often assumed to be
exact to simplify the analysis. However, it is known that in practice all measured quantities
are subject to error, which can deteriorate the overall performance of the network significantly.
This work proposes a new measurement error analysis in the control of multi-agent systems.
In particular, the connectivity preservation of multi-agent systems with state-dependent error
in distance measurements is considered. It is assumed that upper bounds on the measurement
error and its rate of change are available. A general class of distributed control strategies is
then proposed for the distance-dependent connectivity preservation of the agents in the network.
It is shown that if two neighboring agents are initially located in the connectivity range,
they are guaranteed to remain connected at all times. Furthermore, the formation control problem
for a team of single-integrator agents subject to distance measurement error is investigated
using navigation functions. Collision, obstacle and boundary avoidance are important features
of the proposed strategy. Conditions on the magnitude of the measurement error and its rate of
change are derived under which a new error-dependent formation can be achieved anywhere in
the space. The effectiveness of the proposed control strategies in consensus and containment
problems is demonstrated by simulation
