  In this paper, we study the problem of control of discrete-time linear time
varying systems over uncertain channels. The uncertainty in the channels is
modeled as a stochastic random variable. We use exponential mean square
stability of the closed-loop system as a stability criterion. We show that
fundamental limitations arise for the mean square exponential stabilization for
the closed-loop system expressed in terms of statistics of channel uncertainty
and the positive Lyapunov exponent of the open-loop uncontrolled system. Our
results generalize the existing results known in the case of linear time
invariant systems, where Lyapunov exponents are shown to emerge as the
generalization of eigenvalues from linear time invariant systems to linear time
varying systems. Simulation results are presented to verify the main results of
this paper.

Optimization and Control