  We consider remote state estimation of multiple discrete-time linear
time-invariant (LTI) systems over multiple wireless time-varying communication
channels. Each system state is measured by a sensor, and the measurements from
sensors are sent to a remote estimator over the shared wireless channels in a
scheduled manner. We answer the following open problem: what is the fundamental
requirement on the multi-sensor-multi-channel system to guarantee the existence
of a sensor scheduling policy that can stabilize the remote estimation system?
To tackle the problem, we propose a novel policy construction method, and
develop a new analytical approach by applying the asymptotic theory of spectral
radii of products of non-negative matrices. A necessary and sufficient
stability condition is derived in terms of the LTI system parameters and the
channel statistics, which is more effective than existing sufficient conditions
available in the literature. Explicit scheduling policies with stability
guarantees are presented as well. We further extend the analytical framework to
cover remote estimation with four alternative network setups and obtain
corresponding necessary and sufficient stability conditions.
