Controllability and Observability of Linear Discrete-Time Systems with Network Induced Variable Delay

Ionete, Catalin Cosmin; Çela, Arben; Gaïd, Mongi Ben; Réama, Abdellatif

doi:10.3182/20080706-5-kr-1001.00709

Cited by 7 publications

(19 citation statements)

References 13 publications

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“…Note that if the delayed system described by (13) is time invariant, Theorem 2 provides a necessary and sufficient condition for reconstructibility (detectability) of its delayed counterpart. This is reported in for time invariant systems with output delays. It could also be shown by re‐writing reconstructibility (detectability) condition for the delayed system described by (13) as:

([],, \begin{matrix} \overset{C}{true} ((),, italicNp + k - 1 {- \overset{d}{true}}_{y}) \\ \overset{C}{true} ((),, italicNp + k - 2 - {\overset{true˘}{d}}_{y}) \overset{A}{true} ((),, k - {\overset{true˘}{d}}_{y} + italicNp - 1) \\ \begin{matrix} \begin{matrix} ⋮ \\ \overset{C}{true} ((),, k - {\overset{true˘}{d}}_{y}) \overset{A}{true} ((),, k + 1 - {\overset{true˘}{d}}_{y}) \dots \overset{A}{true} ((),, k - {\overset{true˘}{d}}_{y} + italicNp - 1) \end{matrix} \end{matrix} \end{matrix}) w^{j} = ([],, \begin{matrix} \overset{C}{true} \\ ⋮ \\ \begin{matrix} \overset{true˘}{C} \overset{true˘}{A} \\ \begin{matrix} ⋮ \\ \overset{C}{true} {\overset{true˘}{A}}^{italicNp - 1} \end{matrix} \end{matrix} \end{matrix}) w^{j} \neq 0,

which is the same as reconstructibility (detectability) condition of the time invariant system described by (2).…”

Section: Structural Properties Of Ncssmentioning

confidence: 86%

“…References [3-6 ,8] and similar works cited in [3,5] have considered bandwidth limitation modeled by scheduling matrices and studied its effect on structural properties. It is shown that if the communication sequences are admissible (see equations (5)(6)(7)(8) in the present paper), observability will be preserved for a time invariant system subject to bandwidth limitations. For controllability, besides admissibility of the actuator communication sequence, it is required that certain sequences are avoided (see [6] and ch.…”

Section: Introductionmentioning

confidence: 83%

“…Note. If one considers a time invariant system described by (2) instead of the time varying system described by (1), Theorem 1 will reduce to a special case of the result (Th.2) stated in for time invariant systems with input delays. In this case, the aforementioned condition is necessary and sufficient .Theorem A delayed time varying system described by (13) is reconstructible (detectable) for arbitrary finite integer

{\overset{true˘}{d}}_{y} > 0

, if it is reconstructible (detectable) with

{\overset{true˘}{d}}_{y} = 0

.…”

Section: Structural Properties Of Ncssmentioning

confidence: 99%

“…An NCS is characterized by a graph representing components' access to each other, characteristics of individual components, and the shared network [1]. NCS covers several situations, including a fixed topology and constrained communications [4][5][6][7][8][9], a networked multi-agent system in which control [10][11][12][13] or other data processing tasks [14] are distributed between several agents and the topology of network may be subject to changes [10][11][12][13][14], and many other situations [2]. This paper studies the situation in which the network topology is fixed and communication constraints exist in the shared network.…”

Section: Introductionmentioning

confidence: 99%

“…The second concern is guaranteeing that communication constraints (bandwidth limitations, delays, etc.) do not compromise structural properties [4][5][6][7][8][9]. This article studies the second concern, which may be approached assuming different settings of communication constraints.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Structural Properties of Networked Control Systems With Bandwidth Limitations and Delays

Pasand

Montazeri

2017

Asian Journal of Control

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The structural properties of networked control systems with both bandwidth limitations and delays are investigated. Sufficient conditions are given for controllability (stabilizability) and reconstructibility (detectability). Our results enhance previous works by capturing bandwidth limitations and delays simultaneously. The adopted modeling framework could be readily used in control and estimation methods, including optimal and predictive schemes. It also facilitates the use of scheduling optimization algorithms in conjunction with the control scheme presented.

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([],, \begin{matrix} \overset{C}{true} ((),, italicNp + k - 1 {- \overset{d}{true}}_{y}) \\ \overset{C}{true} ((),, italicNp + k - 2 - {\overset{true˘}{d}}_{y}) \overset{A}{true} ((),, k - {\overset{true˘}{d}}_{y} + italicNp - 1) \\ \begin{matrix} \begin{matrix} ⋮ \\ \overset{C}{true} ((),, k - {\overset{true˘}{d}}_{y}) \overset{A}{true} ((),, k + 1 - {\overset{true˘}{d}}_{y}) \dots \overset{A}{true} ((),, k - {\overset{true˘}{d}}_{y} + italicNp - 1) \end{matrix} \end{matrix} \end{matrix}) w^{j} = ([],, \begin{matrix} \overset{C}{true} \\ ⋮ \\ \begin{matrix} \overset{true˘}{C} \overset{true˘}{A} \\ \begin{matrix} ⋮ \\ \overset{C}{true} {\overset{true˘}{A}}^{italicNp - 1} \end{matrix} \end{matrix} \end{matrix}) w^{j} \neq 0,

which is the same as reconstructibility (detectability) condition of the time invariant system described by (2).…”

Section: Structural Properties Of Ncssmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 83%

{\overset{true˘}{d}}_{y} > 0

, if it is reconstructible (detectable) with

{\overset{true˘}{d}}_{y} = 0

.…”

Section: Structural Properties Of Ncssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Structural Properties of Networked Control Systems With Bandwidth Limitations and Delays

Pasand

Montazeri

2017

Asian Journal of Control

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Controllability results for quasi‐linear systems: Standard and descriptor cases

Zhang

Liu

2021

Asian Journal of Control

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This paper investigates the controllability of quasi‐linear systems in standard and descriptor cases. Two extended PBH criteria depending on the coefficient matrices, as sufficient conditions, are proposed to test the controllability of quasi‐linear systems for standard and descriptor cases. Finally, two practical examples are provided to verify the effectiveness of the proposed criteria. The proposed method naturally extends the controllability conclusions to existing results and practically enlightens the study of nonlinear systems.

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Discrete predictor-based event-triggered control of networked control systems

et al. 2019

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A predictor-based controller combined with two event-triggering mechanisms is proposed in order to control an LTI system over a network. The controller is designed in the discrete-time domain which allows to deal with a long sampling period. Similarly large input and output delays can be compensated thanks to the use of a predictor-based method. Two eventtriggering mechanisms, in the sensor-to-controller and controller-to-actuator channels are introduced in order to limit the number of packets sent over the network while preserving the ultimate boundedness of the solutions. The effect of input and output quantization introduced by the network is considered in the stability analysis. The results are illustrated by simulation.

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Controllability and Observability of Linear Discrete-Time Systems with Network Induced Variable Delay

Cited by 7 publications

References 13 publications

Structural Properties of Networked Control Systems With Bandwidth Limitations and Delays

Structural Properties of Networked Control Systems With Bandwidth Limitations and Delays

Controllability results for quasi‐linear systems: Standard and descriptor cases

Discrete predictor-based event-triggered control of networked control systems

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