  In this paper, we study the simultaneous stability problem of a finite number
of locally inter-connected linear subsystems under practical constraints,
including asynchronous and aperiodic sampling, time-varying delays, and
measurement errors. We establish a new Lyapunov-based stability result for such
a decentralized system. This system has a particular simple structure of
interconnections, but it captures some key characteristics of a large class of
intermediate models derived from the consensus analysis of multi-agent systems.
The stability result is applicable to the estimation of the maximum allowable
inter-sampling periods and time delays based on individual dynamics and
coupling structures in the scenarios of consensus control via asynchronous
sampling of relative states and asynchronous broadcasting of self-sampled
states respectively. The asynchrony of aperiodic sampling and the existence of
measurement errors allow the utilization of some kinds of quantizing devices,
such as Logarithmic quantizers, in the process of data sampling, and allow the
introduction of a period of dwell time after each update of state measurement
to eliminate the Zeno behavior of events in event-based control. The extension
in the case with input saturations and input delays is also discussed.
