Stability of linear feedback systems with random communication delays

Abstract

Integral control of large-scale systems implies coordination of actrvities by information exchange via communication networks. Usually these networks are shared with other users. Thus traffic conditions in the network may introduce time-varying random delays in the control loop with adverse effects on its performance and stability. Hence, the control must be designed to compensate for these delays. Recent work in modelling integrated control and communication systems has shown that the communication specific phenomena inducing random communication delays (such as multirate sampling, vacant sampling and message rejection) may be encompassed by finite-dimensional linear discrete-time models, provided that the plant and the controller are linear and time invariant. Existing approaches to the design of integrated control systems rely on conservative stability tests, because only sufficient stability conditions were found for systems with random time-varying delays. In this paper, necessary and sufficient conditions are found for zero-state mean-square exponential stability of the considered class of control systems. Numerical tests for zero-state stability are outlined and illustrated by a simple example. Finally, the results are also demonstrated on specific hardware, a multiprocessor real-time control network which has been recently developed.

Output feedback stochastic H∞ stabilization of networked fault-tolerant control systems

“…One way is to model the transitions of the random delays r sk as a finite state Markov process [20,29,33]. In this case we have…”

“…It is noticed that in all of the aforementioned papers, the plant is in the continuous-time domain. For the discrete-time case, in [20] and [29], the network-induced random delays were modeled as Markov chains such that the closed-loop system is a jump linear system with one mode. The class of linear systems with Markovian jumping parameters has attracted increasing attention in the recent literature.…”

Intelligent Controller for Networked Control Systems with Time-delay

“…따라서 시간지연 및 불확실성에 대한 안정 성 연구에 관한 연구가 활발히 진행되어 왔다 [1][2][3][4][5][6][7][8][9][10][11]. [1][2][3][4][5]에 서는 네트워크에 의한 시간지연을 제어기 설계시 명시적으 로 고려하였다. [7]에서는 폐루프 시스템의 시간지연을 시 변이라고 가정하고, 샘플링 한 주기보다 작다고 가정하였 다.…”

Experimental Testing of TCP/IP/Ethernet Communication for Automatic Control

“…The control theory proposes some analytical discussions of the problem of delays introduced by networking in control systems -see e.g. [7], [8], [9], [10].…”