Christopher M. Kellett

Smooth Lyapunov functions and robustness of stability for difference inclusions

We demonstrate the equivalence of robust global asymptotic stability (GAS) of the origin and the existence of a smooth Lyapunov function for difference inclusions defined by upper semicontinuous set-valued maps. Sufficient conditions for robust GAS are given. As an application of these results, we give conditions for robust GAS of difference equations defined by discontinuous right-hand sides.

On the Robustness of

We consider stability with respect to two measures of a difference inclusion, i.e., of a discrete-time dynamical system with the push-forward map being set-valued. We demonstrate that robust stability is equivalent to the existence of a smooth Lyapunov function and that, in fact, a continuous Lyapunov function implies robust stability. We also present a sufficient condition for robust stability that is independent of a Lyapunov function. Toward this end, we develop several new results on the behavior of solutions of difference inclusions. In addition, we provide a novel result for generating a smooth function from one that is merely upper semicontinuous.

\mathcalKL

The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and compress-forward are shown to be bounded away from the cut-set upper bound at high signal-to-noise ratios (SNR). It is known that the gap between the compress-forward rate and the capacity upper bound is a constant at high SNR, and that between the complete-decode-forward rate and the upper bound increases with SNR at high SNR. In this paper, a functional-decode-forward coding strategy is proposed. It is shown that for L ≥ 3, complete-decode-forward achieves the capacity when SNR ≤ 0 dB, and functional-decode-forward achieves the capacity when SNR ≥ 0 dB. For L = 2, functional-decode-forward achieves the capacity asymptotically as SNR increases.

-stability for Difference Inclusions: Smooth Discrete-Time Lyapunov Functions

We demonstrate the existence of a smooth control-Lyapunov function (CLF) for difference equations asymptotically controllable to closed sets. We further show that this CLF may be used to construct a robust feedback stabilizer. The existence of such a CLF is a consequence of a more general result on the existence of weak Lyapunov function under the assumption of weak asymptotic stability of a closed (not necessarily compact) set for a difference inclusion.

Capacity Theorems for the AWGN multi-way relay channel

Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set

Discrete-time asymptotic controllability implies smooth control-Lyapunov function

{\cal A}

Weak Converse Lyapunov Theorems and Control-Lyapunov Functions

for a differential inclusion that is defined on

Distributed and Decentralized Control of Residential Energy Systems Incorporating Battery Storage

\mathbb{R}^n

Further results on robustness of (possibly discontinuous) sample and hold feedback

, is locally Lipschitz on

Adaptive tuning of drop-tail buffers for reducing queueing delays

\mathbb{R}^n \backslash {\cal A}