Practical partial stability of time-varying systems

<p style='text-indent:20px;'>In this paper we investigate the practical asymptotic and exponential partial stability of time-varying nonlinear systems. We derive some sufficient conditions that guarantee practical partial stability of perturbed systems using Lyapunov's theory where a converse theorem is presented. Therefore, we generalize some works which are already made in the literature. Furthermore, we present some illustrative examples to verify the effectiveness of the proposed methods.</p>

A remark on a converse theorem of Cogdell and Piatetski-Shapiro

In this paper, we reprove a global converse theorem of Cogdell and Piatetski-Shapiro using purely global methods.

A Strong Converse Theorem for Hypothesis Testing Against Independence over a Two-Hop Network

By proving a strong converse theorem, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by combining two recently-proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verdú (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft information costs. The techniques used in our paper can also be applied to prove strong converse theorems for other multiterminal hypothesis testing against independence problems.