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Numeric and Analytic Investigations of Mean-Square Exponential Stability for Stochastically Timed Systems

[+] Author Affiliations
Dylan Poulsen

Washington College, Chestertown, MD

Ian Gravagne, John M. Davis

Baylor University, Waco, TX

Paper No. DSCC2015-9810, pp. V001T02A005; 6 pages
doi:10.1115/DSCC2015-9810
From:
  • ASME 2015 Dynamic Systems and Control Conference
  • Volume 1: Adaptive and Intelligent Systems Control; Advances in Control Design Methods; Advances in Non-Linear and Optimal Control; Advances in Robotics; Advances in Wind Energy Systems; Aerospace Applications; Aerospace Power Optimization; Assistive Robotics; Automotive 2: Hybrid Electric Vehicles; Automotive 3: Internal Combustion Engines; Automotive Engine Control; Battery Management; Bio Engineering Applications; Biomed and Neural Systems; Connected Vehicles; Control of Robotic Systems
  • Columbus, Ohio, USA, October 28–30, 2015
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5724-3
  • Copyright © 2015 by ASME

abstract

This paper is motivated by the problems posed in feedback control design when actuators, sensors, and/or computational nodes connect via unreliable or unpredictable communications channels. In these cases, there is a degree of stochastic uncertainty to the timing of the system’s discretizing elements, such as digital-to-analog converters. Several theorems related to the stability of non-uniformly sampled discrete dynamical systems have recently been proposed; here we examine through numeric investigation the characteristics of systems which are mean square exponentially stable (MSES). In particular we present a method to compute the range of mean and variance that a nonuniformly discretized feedback control system may tolerate while remaining MSES. Several examples are presented.

Copyright © 2015 by ASME
Topics: Stability

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