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In this paper, we study the problem of control of discrete-time linear timevarying systems over uncertain channels. The uncertainty in the channels ismodeled as a stochastic random variable. We use exponential mean squarestability of the closed-loop system as a stability criterion. We show thatfundamental limitations arise for the mean square exponential stabilization forthe closed-loop system expressed in terms of statistics of channel uncertaintyand the positive Lyapunov exponent of the open-loop uncontrolled system. Ourresults generalize the existing results known in the case of linear timeinvariant systems, where Lyapunov exponents are shown to emerge as thegeneralization of eigenvalues from linear time invariant systems to linear timevarying systems. Simulation results are presented to verify the main results ofthis paper.

Stabilization of linear time varying system over uncertain channels