Performance limits in the control of single‐input linear time‐invariant plants over fading channels

Maass, Alejandro I.; Silva, Eduardo I.

doi:10.1049/iet-cta.2013.0888

Cited by 16 publications

(6 citation statements)

References 44 publications

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“…k . This lemma is also the multichannel counterpart of the theorems in the works of Maass and Silva [29] and of Silva and Solis [40], and the corresponding discrete counterpart of Lemma 1 is given in [39]. Thus, the proof is omitted.…”

Section: Equivalence Relationmentioning

confidence: 92%

“…The main difference between our work and the literature [25]- [27] is that we address the stabilization problem for discrete-time NCSs. Formally, this article is a generalization of [25], [28], [29], but the difficulties in solving the discretetime case are as follows: 1) Since the open-loop system topological entropy is inconsistent for the definitions of a continuous-time system and a discrete-time system, i.e., the sum of the unstable poles for a continuous-time plant and the logarithm of the product of the modulus of the unstable poles for a discrete-time plant, the proof methods used for the continuous-time system cannot be directly applied to the discrete-time plant, and other methods must be used to address stabilization of NCSs with configurable channel resources. 2) In particular, when discussing the sufficient and necessary conditions for stabilizing the networked system under fixed resources and because the open-loop system topological entropy is inconsistent with the definitions of a continuous-time system and a discrete-time system, a necessary and sufficient condition is given for the continuoustime system.…”

Section: Introductionmentioning

confidence: 99%

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Mean Square Stabilization of Multi-Input Discrete-Time Systems Over Stochastic Multiplicative and Additive White Gaussian Noise Channels

Shen

2020

IEEE Access

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This paper studies mean square stabilization for multi-input discrete-time systems over a general fading channel, and the channel is modeled as a cascade of multiplicative noise and white Gaussian additive noise. The main objective is to determine the minimum mean capacity required to enable stabilization. The basic idea of our method is to consider stabilization from the viewpoint of a supply/demand balance. Specifically, for communication resources, each system control input is viewed as the demand side, while the channel is viewed as the supply side, and the supply resource of the channel is characterized by the mean square capacity of each channel. Stabilization of the networked control system requires the balance of supply and demand. Based on whether the channel resources are configurable, two different methods for balancing the supply and the demand are discussed. If the channel resources are configurable, the demand side can be satisfied by adjusting the supply side (channel resources); otherwise, the demand side (a certain transceiver design mechanism) can be adjusted to meet the requirements of the supplier. For both cases, sufficient and necessary conditions for stabilizing discrete-time networked control systems are given. INDEX TERMS mean square stabilization; general fading channel; multi-input discrete-time systems

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Section: Equivalence Relationmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Mean Square Stabilization of Multi-Input Discrete-Time Systems Over Stochastic Multiplicative and Additive White Gaussian Noise Channels

Shen

2020

IEEE Access

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“…Moreover, it is not hard to verify that (40) holds for all channel uncertainties modeled by multiplicative white noises with zero mean and variance σ 2 .…”

Section: Then It Holds To the Impulse Response Of The Channel Uncerta...mentioning

confidence: 99%

Mean-Square Input-Output Stability and Stabilizability of a Networked Control System with Random Channel Induced Delays

Su,

Li,

2021

Preprint

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This work mainly investigates the mean-square input-output stability and stabilizability for a single-input single-output (SISO) networked linear feedback system. The control signal in the networked system is transmitted over an unreliable channel. In this unreliable channel, the data transmission times, referred to as channel induced delays, are random values and the transmitted data could also be dropout with certain probability. The channel induced delays and packet dropout are modeled by an independent and identically distributed (i.i.d.) stochastic process with a fixed probability mass function (PMF). It is assumed that the transmitted data are with time stamps. At the channel terminal, a linear combination of data received at one sampling time is applied to the plant of the networked feedback system as a new control signal. To describe the uncertainty in the channel, a concept so called frequency response of variation is introduced for the unreliable channel. With the given linear receiving strategy, a mean-square input-output stability criterion is established in terms of the frequency response of variation of the unreliable channel for the networked feedback system. It is shown by this criterion that the mean-square input-output stability is determined by the interaction between the frequency response of variation and the nominal feedback system. In the mean-square input-output stability of the system, the role played by the random channel induced delays is the same as that played by a colored additive noise in an additive noise channel with a signal-to-noise ratio constraint. Moreover, the mean-square input-output stabilizability via output feedback is studied for the networked system. When the plant in the networked feedback system is minimum phase, an analytic necessary and sufficient condition is presented for its mean-square input-output stabilizability. It turns out that the stabilizability is only determined by the interaction between the frequency response of variation of the channel and unstable poles of the plant. Finally, numerical examples are given to illustrate our results.

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“…Meanwhile numerous special issues on NCSs have been concerned by many researchers, inspired by wide applications of NCSs in cooperative vehicles [4, 5], sensor networks [6, 7], multi‐agent systems [8, 9] and so on. In NCSs, the imperfect communication channels can introduce various constraints and uncertainties, for instance, packet dropouts [10, 11], time delays [12, 13], fading [14, 15], limited data rates [16, 17] and quantisation [18, 19] etc.…”

Section: Introductionmentioning

confidence: 99%

Stochastic LQ control under asymptotic tracking for discrete systems over multiple lossy channels

Ling

Feng

Claveau

et al. 2019

IET Control Theory & Applications

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Performance limits in the control of single‐input linear time‐invariant plants over fading channels

Cited by 16 publications

References 44 publications

Mean Square Stabilization of Multi-Input Discrete-Time Systems Over Stochastic Multiplicative and Additive White Gaussian Noise Channels

Mean Square Stabilization of Multi-Input Discrete-Time Systems Over Stochastic Multiplicative and Additive White Gaussian Noise Channels

Mean-Square Input-Output Stability and Stabilizability of a Networked Control System with Random Channel Induced Delays

Stochastic LQ control under asymptotic tracking for discrete systems over multiple lossy channels

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