Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach
In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send i...
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| Vydané v: | IEEE transactions on automatic control Ročník 56; číslo 9; s. 2101 - 2115 |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY
IEEE
01.09.2011
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 0018-9286, 1558-2523 |
| On-line prístup: | Získať plný text |
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| Abstract | In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called "periodic" and "quadratic" protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature. |
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| AbstractList | In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called "periodic" and "quadratic" protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature. |
| Author | Donkers, M. C. F. Heemels, W. P. M. H. Hetel, L. van de Wouw, N. |
| Author_xml | – sequence: 1 givenname: M. C. F. surname: Donkers fullname: Donkers, M. C. F. email: m.c.f.donkers@tue.nl organization: Mech. Eng. Dept., Eindhoven Univ. of Technoloy, Eindhoven, Netherlands – sequence: 2 givenname: W. P. M. H. surname: Heemels fullname: Heemels, W. P. M. H. email: m.heemels@tue.nl organization: Mech. Eng. Dept., Eindhoven Univ. of Technoloy, Eindhoven, Netherlands – sequence: 3 givenname: N. surname: van de Wouw fullname: van de Wouw, N. email: n.v.d.wouw@tue.nl organization: Mech. Eng. Dept., Eindhoven Univ. of Technoloy, Eindhoven, Netherlands – sequence: 4 givenname: L. surname: Hetel fullname: Hetel, L. email: laurentiu.hetel@ec-lille.fr organization: Lab. d'Autom., Genie Inf. et Signal (LAGIS), Lille, France |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24554392$$DView record in Pascal Francis https://hal.science/hal-00622934$$DView record in HAL |
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| Copyright | 2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Sep 2011 Distributed under a Creative Commons Attribution 4.0 International License |
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| Keywords | Polytope time-varying systems Continuous time Linear time networked control systems (NCSs) Modeling Local network Hybrid system Time varying system Chemical reactor Uncertain system switched systems Network analysis Linear matrix inequality Time interval Lower bound Multimodel control Stability uncertain systems Transmission protocol Delay system Distributed system Communication network Transmission time Communication constraints Discrete time Distributed control |
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| Snippet | In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission... |
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| SubjectTerms | Applied sciences Automatic Communication constraints Computer science; control theory; systems Computer systems and distributed systems. User interface Control system analysis Control systems Control theory. Systems Controllers Delay Engineering Sciences Exact sciences and technology Intervals networked control systems (NCSs) Networks Process control. Computer integrated manufacturing Protocols Software Stability Stability analysis Stability criteria Studies switched systems Switches Switching theory System theory time-varying systems Uncertain systems |
| Title | Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach |
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