An improved stability criterion for linear time-varying delay systems

Feng, Wenxi; Luo, Fei; Duan, Wenyong; Li, Yan; Chen, Jian

doi:10.1080/00051144.2019.1706885

Cited by 5 publications

(3 citation statements)

References 42 publications

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“…Mathematical models of time-delay systems belong to the category of functional di erential equations (4). e essential di erence from ordinary di erential equations is that functional differential equations describing time-delay systems are in nite-dimensional "with memory", while ordinary differential equations are nite-dimensional "memoryless" [5].…”

Section: Introductionmentioning

confidence: 99%

Study on Hopf Branch of Stability of Time-Delay Unified System and Performance Evaluation Based on Deep Learning

2022

Mathematical Problems in Engineering

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Deep learning is a breakthrough in machine learning research. It aims to establish a deep network structure that can simulate the human brain for analysis and learning, interpret data through the mechanism of layer-by-layer abstract feature representation, and has excellent feature learning capabilities. According to the input-output performance evaluation data of colleges and universities, three experiments are done. First, the feature expression ability of RBM, the basic building block of deep learning, is studied, and compared with PCA, the results show that RBM-fine-tuning has better performance than PCA-expressed classifier; the reconstruction error can be used to judge the hidden layer. As the number of RBM layers increases, the classification accuracy gradually increases, indicating the feasibility of the RBMs feature extractor. Second, the model in this study has a higher prediction accuracy than other classification models and clarifies the effectiveness of the modular deep learning model based on RBMs from the perspectives of network convergence analysis and network output analysis. The ability is stronger than DBN, and the obtained abstract feature representation is more conducive to classification. Although the classification accuracy rate of the model in this study has been improved, the model has certain limitations. The network initialization is still set based on experiments and experience, and the prediction accuracy rate is only 88.3%, which needs to be improved. The parameter training algorithm of RBMs can be further studied. To improve the more accurate reference basis for the performance evaluation of colleges and universities. Third, in the research of dynamical systems, the stability of the time-delay unified system at zero equilibrium and positive equilibrium is studied, and the conditions for generating the Hopf branch are given. At the same time, some conclusions are obtained through theoretical analysis. Numerical simulations further verify the validity of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Study on Hopf Branch of Stability of Time-Delay Unified System and Performance Evaluation Based on Deep Learning

2022

Mathematical Problems in Engineering

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“…For the construction of LKF, a LKF with the delay decomposition method [22][23][24], LKF with multiple integral items [25][26][27][28][29] and LKF with some augmented vectors [30,31] are proposed. On the other aspect, the Jensen inequality [32], B-L inequality [33] and relaxed integral inequality techniques [34][35][36][37][38] are used to estimate the upper bound of the derivative of LKF. In order to reduce the conservativeness of the LKF construction, a lot of coupling information between the system state variables and time delays is introduced into the LKF, which leads to some nonlinear terms in the final results.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Stability Criteria of Network-Based Load Frequency Control of Power Systems with Time-Varying Delays

et al. 2021

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The stability problem for load frequency control (LFC) of power systems with two time-varying communication delays is studied in this paper. The one-area and two-area LFC systems are considered, respectively, which are modeled as corresponding linear systems with additive time-varying delays. An improved stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, an augmented LKF consisting of delay-dependent matrices and some single-integral items containing time-varying delay information in two different delay subintervals is constructed, which makes full use of the coupling information between the system states and time-varying delays. Secondly, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequality to the linear matrix inequality (LMI) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some numerical examples are presented to show the improvement of the proposed approach.

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“…Jensen inequality and B-L inequality were proposed in Gu (2000) and Seuret and Gouaisbaut (2015), respectively, where a tight upper bound of the derivative of the LKFs was obtained. Zhang et al (2017a); Duan et al (2018); Duan et al (2019b); Feng et al (2020); Kwon and Lee (2021) reduced the conservatism of the stability criterion via some relaxed integral inequality techniques. Recently, a novel negative definite inequality equivalent transformation lemma was proposed in Fúlvia et al (2020), which improved the degree of freedom for solving the LMI in the main theorem without introducing extra conservatism.…”

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confidence: 99%

Optimization and H∞ Performance Analysis for Load Frequency Control of Power Systems With Time-Varying Delays

Su¹,

Li²,

Chen³

et al. 2021

Front. Energy Res.

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With the development and expansion of the power grid, the load frequency control (LFC) scheme receives sensor signals and outputs control signals through an open communication network with a mass of data and extensive information exchange, which may introduce constant, and time-varying delays. This paper considers the optimization and H∞ performance problem for LFC of power systems with time-varying delays. Some improved criteria for guaranteeing the stability and H∞ performance of the closed-loop system with unknown external load disturbances via the Lyapunov stability theory application. An unique delay-dependent proportional-integral (PI) controller and an optimized PI controller are designed for a specified H∞ performance index and set, respectively. The criteria proposed in this paper are based on linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI-Toolbox. Finally, in case studies, the effectiveness of our method is demonstrated.

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An improved stability criterion for linear time-varying delay systems

Cited by 5 publications

References 42 publications

Study on Hopf Branch of Stability of Time-Delay Unified System and Performance Evaluation Based on Deep Learning

Study on Hopf Branch of Stability of Time-Delay Unified System and Performance Evaluation Based on Deep Learning

Enhanced Stability Criteria of Network-Based Load Frequency Control of Power Systems with Time-Varying Delays

Optimization and H∞ Performance Analysis for Load Frequency Control of Power Systems With Time-Varying Delays

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