Stability analysis of time-delay systems via free-matrix-based double integral inequality

Chen, Hua; Wu, Shuangshuang; Guan, Xinping

doi:10.1080/00207721.2016.1177132

Cited by 36 publications

(17 citation statements)

References 23 publications

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“…Time delays affect systems dynamics in many engineering applications like chemical control systems, biology, and medicine [1,2]. Delays are also encountered in communication and information technologies like high-speed communication networks [3]. It should be noted that time delay may be, in some applications like communication lines, a source of instability and performance degradation [4].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Bouafoura

Braïek

2019

Complexity

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The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

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Section: Introductionmentioning

confidence: 99%

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Bouafoura

Braïek

2019

Complexity

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“…[5][6][7]11,14,[16][17][18][19][20][21][22][23][24][25][26][27][28][29]33], and the references therein). [5][6][7]11,14,[16][17][18][19][20][21][22][23][24][25][26][27][28][29]33], and the references therein).…”

Section: Introductionunclassified

“…As a consequence, a set of related research results based on the L-K framework had been put forward in the literature. For instance, see the free-weighting matrix approach [4], augmented L-K functional approach [5], reciprocally convex approach [6], and the integral inequality approach [7][8][9][10][12][13][14][15]34]. Just recently, a relaxed conditions L-K functional approach has been proposed by Lee et al in [35].…”

Section: Introductionmentioning

confidence: 99%

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New Augmented Lyapunov‐Krasovskii Functional for Stability Analysis of Systems with Additive Time‐Varying Delays

Ding¹,

He²,

Wu³

et al. 2017

Asian Journal of Control

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This paper is concerned with stability analysis for continuous-time systems with additive time-varying delays in the Lyapunov-Krasovskii(L-K) framework. Firstly, in view of the relationships between the upper bounds of the two time-varying delays, a new augmented L-K functional is constructed by using the information of the two upper bounds. Secondly, the free-matrix-based integral inequality is used to estimate the derivative of the constructed L-K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.

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“…(ii) Recently, some new approaches have been developed for the stability analysis of delayed neural networks, which can be applied into the generalized 2 filtering problem of neural networks, such as the delaydecomposition approach [21] and the free-matrixbased double integral inequality [22].…”

Section: Remarkmentioning

confidence: 99%

Improved GeneralizedH2Filtering for Static Neural Networks with Time-Varying Delay via Free-Matrix-Based Integral Inequality

2018

Mathematical Problems in Engineering

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This paper focuses on the generalized 2 filtering of static neural networks with a time-varying delay. The aim of this problem is to design a full-order filter such that the filtering error system is globally asymptotically stable with guaranteed 2 performance index. By constructing an augmented Lyapunov-Krasovskii functional and applying the free-matrix-based integral inequality to estimate its derivative, an improved delay-dependent condition for the generalized 2 filtering problem is established in terms of LMIs. Finally, a numerical example is presented to show the effectiveness of the proposed method.

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Stability analysis of time-delay systems via free-matrix-based double integral inequality

Cited by 36 publications

References 23 publications

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

New Augmented Lyapunov‐Krasovskii Functional for Stability Analysis of Systems with Additive Time‐Varying Delays

Improved GeneralizedH2Filtering for Static Neural Networks with Time-Varying Delay via Free-Matrix-Based Integral Inequality

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