Vsevolod Shneer

Brief paper: Stability analysis of stochastic networked control systems

In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet-dropouts and communication constraints. Communication constraints impose that, per transmission, only one sensor or actuator node can access the network and send its information. Which node is given access to the network at a transmission time is orchestrated by a so-called network protocol. This paper considers NCSs, in which the transmission intervals and transmission delays are described by a random process, having a continuous probability density function (PDF). By focussing on linear plants and controllers and periodic and quadratic protocols, we present a modelling framework for NCSs based on stochastic discrete-time switched linear systems. Stability (in the mean-square) of these systems is analysed using convex overapproximations and a finite number of linear matrix inequalities. On a benchmark example of a batch reactor, we illustrated the effectiveness of the developed theory.

Large deviations for random walks under subexponentiality: The big-jump domain

For a given one-dimensional random walk {Sn} with a subexponential step-size distribution, we present a unifying theory to study the sequences {xn} for which as n→∞ uniformly for x≥xn. We also investigate the stronger “local” analogue, . Our theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.

Estimates for the Distributions of the Sums of Subexponential Random Variables

AbstractLet

Stochastic Stability of Monotone Economies in Regenerative Environments

\left\{ {S_n } \right\}_{n \geqslant 1}

Stability analysis of stochastic Networked Control Systems

be a random walk with independent identically distributed increments

A random multiple-access protocol with spatial interactions

\left\{ {\xi _i } \right\}_{i \geqslant 1}