An Improved Reciprocally Convex Inequality and Application to Stability Analysis of Time-Delay Systems Based on Delay Partition Approach

Xue, Yuncan; Li, Haifang; Yang, Xiaona

doi:10.1109/access.2018.2854563

Cited by 8 publications

(2 citation statements)

References 33 publications

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“…From the research on digital filters point of view, there are only a few works on digital filters considering the time-varying delay [3], [47], [49], [50], and the techniques used therein are all conservative in comparison to the ones developed for the time-delay systems. Recently, many more effective methods have been developed for dealing with time-varying delays, such as augmented Lyapunov functionals [51]- [53], new inequalities [42], [54]- [56], extended reciprocally convex matrix inequalities [57]- [59], etc. From the viewpoint of techniques dealing with the discrete-time delay systems, every term in the Lyapunov functionals is usually required to positive in order to guarantee the positive-definiteness of the functionals.…”

Section: Introductionmentioning

confidence: 99%

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

Chen

Zhang

et al. 2022

IEEE Access

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This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

Chen

Zhang

et al. 2022

IEEE Access

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“…For the former methods mentioned above, the main methods for constructing LKFs are the complete LKF [19], discrete type LKF [20], augmented LKF [21]- [24], and delay partition methods [25]- [27]. For the latter, the prime methods are the free-weighting matrix approach [28], integral inequalities [29]- [35], reciprocally convex approach [36]- [39], and the quadratic function method [40]- [42].…”

Section: Introductionmentioning

confidence: 99%

A New Relaxed Lyapunov-Krasovskii Functional for Stability Analysis of Time-Varying Delay Systems

Ding

et al. 2021

IEEE Access

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In this paper, the stability analysis problem of time-varying delay systems was studied. Based on recent research on Lyapunov-Krasovskii functionals (LKFs), relaxed conditions have been found to weaken some matrices in terms of LKFs, which means that some integral terms cannot be strictly positive definite. Therefore, motivate by this consideration, a new relaxed condition was constructed to weaken some matrices in constructed LKF. Then, for the sake of obtaining more information of time delays, dynamic delay interval (DDI) method was introduced to address the double integral terms with time-varying delay. Furthermore, some recent technologies were employed to process derivatives of LKF. As a consequence, a less conservative result was obtained. The examples given by previous papers were used to demonstrate the superiority of our work. INDEX TERMSRelaxed condition; Lyapunov-Krasovskii functional(LKF); stability analysis; timevarying delay systems.

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Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma

Wang

Chen

Park

et al. 2023

Applied Mathematics and Computation

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An Improved Reciprocally Convex Inequality and Application to Stability Analysis of Time-Delay Systems Based on Delay Partition Approach

Cited by 8 publications

References 33 publications

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

A New Relaxed Lyapunov-Krasovskii Functional for Stability Analysis of Time-Varying Delay Systems

Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma

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