Stabilization of linear time varying system over uncertain channels

TL;DR

This paper investigates the stabilization of discrete-time linear time-varying systems over uncertain channels, establishing fundamental limitations based on channel uncertainty statistics and Lyapunov exponents, with simulation validation.

Contribution

It generalizes existing LTI system stabilization results to LTV systems by linking mean square exponential stabilization to channel uncertainty and Lyapunov exponents.

Findings

Fundamental limitations for stabilization derived

Lyapunov exponents generalize eigenvalues for LTV systems

Simulation confirms theoretical results

Abstract

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.