Stability Analysis and Synthesis for Networked Systems with Noisy Sampling Intervals, Random Transmission Delays and Packet Dropouts

In this article, we study the stability analysis and <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> controller synthesis problems for networked systems with random transmission delays and packet dropouts that are subject to noisy...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 69; no. 2; pp. 1 - 8
Main Authors: Hu, Zhipei, Deng, Feiqi, Su, Yongkang, Luo, Shixian, Liu, Yu, Chen, Kai
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> H_{\infty }</tex-math> </inline-formula> control
Algorithms
Closed loops
Continuity (mathematics)
Control systems design
Controllers
Coupling
Courthouses
Delays
Discrete time systems
Intervals
Matrix decomposition
Networked systems
Noise measurement
noisy sampling intervals
Nonlinearity
packet dropouts
random transmission delays
Random variables
Randomness
Sampled data systems
Sampling
Stability analysis
Stability augmentation
Stochastic systems
Synthesis
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this article, we study the stability analysis and <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> controller synthesis problems for networked systems with random transmission delays and packet dropouts that are subject to noisy sampling intervals. The sampling errors and transmission delays are described by an independent and identically distributed sequence of continuous random variables and the transmission delays are assumed to be smaller than the noisy sampling intervals. First, a closed-loop discrete-time stochastic framework for networked system that allows investigating noisy sampling intervals, random transmission delays and packet dropouts simultaneously is established. To render the discrete-time stochastic system suitable for stability analysis and synthesis, an equivalent yet tractable stochastic augmented model is then reformulated with the help of matrix exponential computation. Based on this augmented model, a stability condition involving the expectation of a nonlinear and random coupling matrix is derived. By recurring to the law of total expectation and Kronecker product operation, the expectation operation of the coupling matrix subject to high nonlinearity and multiple randomness is decoupled. Subsequently, a controller algorithm is designed such that the exponential mean-square stability of the original discrete-time stochastic system with a prescribed <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> performance is guaranteed. Finally, an example is provided to illustrate the effectiveness of the controller design algorithm.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3282849