Improved Stabilization for Continuous Dynamical Systems with Two Additive Time‐Varying Delays

Xiong, Lianglin; Zhou, Wei

doi:10.1002/asjc.1124

Cited by 11 publications

(8 citation statements)

References 36 publications

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“…Therefore, it is clearly that the approach in [14] for designing controller is more flexible, and this example shows the effectiveness of our methods presented in this paper.…”

Section: Numerical Examplesmentioning

confidence: 65%

“…So, the research about the synthesis problem for MJSs will become more complex and difficult. In addition, delay systems are frequently encountered in various practical systems, such as engineering, biology, economics, neural networks, and network control, [9][10][11][12][13][14][15][16], however, this class system is instability and performance deterioration in many cases. Thus, recent past decades have witnessed extensive research on delay systems in the literature, including stability analysis, stabilization H∞ controller design, robust filtering analysis, and model reduction or simplification [17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Stabilization for Markovian Jump Systems with Additive Time-varying Delays

Zhang¹,

Qiu²,

Xiong³

et al. 2018

Proceedings of the 2017 2nd International Conference on Electrical, Control and Automation Engineering (ECAE 2017)

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Abstract-In this paper, the problem of stabilization for Markovian jump systems with additive time-varying delays is considered. First of all, by constructing a new Lyapunov functional with triple integral terms, using new inequalities, convex combination technique and combining with other analytical techniques, the stochastically stability and stabilization conditions of the Markovian jump systems in terms of linear matrix inequalities with lower conservatism are obtained. Then, the controller of the closed-loop system is designed by the transformation technique of inequalities. Finally, a numerical example is given to verify the effectiveness of the provided method and the superiority of the results.

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“…Therefore, it is clearly that the approach in [14] for designing controller is more flexible, and this example shows the effectiveness of our methods presented in this paper.…”

Section: Numerical Examplesmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Stabilization for Markovian Jump Systems with Additive Time-varying Delays

Zhang¹,

Qiu²,

Xiong³

et al. 2018

Proceedings of the 2017 2nd International Conference on Electrical, Control and Automation Engineering (ECAE 2017)

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“…To overcome this issue mentioned above, we consider the AETM which can be effectively reduce the total number of released data into the network. Remark 5 Consider the system (15) with absence of T–S fuzzy, uncertainties

false(i . e . normalΔ A = normalΔ A_{d} = normalΔ B = normalΔ D = 0 false)

, and there is no extended dissipative. Moreover, for the general system one has accomplished a few results in [8, 10], we get

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \dot{m} (t) & = A m (t) + A_{d} m (t - κ (t)) + B u (t) . \end{matrix}

As per Theorem 1, the delay‐dependent stability of system (44) is shown in the subsequent Corollary 1. Corollary 1 For a given scalars

κ_{1}, κ_{2}, μ_{1}, μ_{2}

and h , the system (44) is asymptotically stable, if there exist matrices

P > 0, {\bar{Q}}_{i} > 0, i = 1, 2, 3, 4, {\hat{R}}_{1} > 0, {\hat{R}}_{2} > 0, S_{j} > 0, j = 1, 2, 3, \dots, 7, {\bar{Q}}_{6} > 0, {\overset{false¯}{normalΦ}}_{1} > 0, {\overset{false¯}{normalΦ}}_{2} > 0, \overset{false¯}{K}

and

…”

Section: Resultsmentioning

confidence: 99%

“…To exhibit the advantage of our technique, we consider system (44) with the subsequent parameters:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ A & = [\begin{matrix} center center1em4pt \\ 2 & 0 \\ 0 & 0.9 \end{matrix}], A_{d} = [\begin{matrix} center center1em4pt \\ - 1 & 0 \\ - 1 & - 1 \end{matrix}], B = [\begin{matrix} center center1em4pt \\ 1 & - 2 \\ - 1.2 & 0.8 \end{matrix}], \\ {\dot{k}}_{1} (t) \leq 0.1, {\dot{k}}_{2} (t) \leq 0.8 . \end{matrix}

In this paper,

κ_{1}

and

κ_{2}

represent the delay upper bound of

κ_{1} false(t false)

and

κ_{2} false(t false)

, respectively. We calculated delay bounds for various cases by utilising Corollary 1, and the stability criteria in [8, 10], MAUBs are listed in Table 1. From this Table 1, one can clearly observe that the strategy and procedures (RII, SAFBII, and DAFBII) of this paper can give less conservative results than in [8, 10].…”

Section: Comparison Examplementioning

confidence: 99%

“…Therefore, taking the model with STD components into consideration is meaningful. In the process of our research on this subject, we find that there is still much room for further development of the existing results [7–10]. Recently, the relaxed and auxillary function based integral inequalities plays an important role in the stability criteria for time‐delay systems [11, 12].…”

Section: Introductionmentioning

confidence: 99%

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Robust event‐triggered T–S fuzzy system with successive time‐delay signals and its application

Vadivel

Joo

2020

IET Control Theory & Appl

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This study isrelevant to the topic of a robust event‐triggered mechanism for the Takagi–Sugeno (T–S) fuzzy system with successive time‐delay (STD) signals and its application, where the uncertainties satisfy the randomly occurring form. Firstly, an event‐triggered communication scheme is introduced, which can adaptively adjust the communication threshold to save limited communication resource. The primary aim of this study is to model an event‐triggered mechanism with STD, which ensures that the suggested T–S fuzzy system achieves extended dissipative with permissible uncertainties. Secondly, by using the relaxed integral inequality technique, single and double auxillary function‐based integral inequalities to evaluate the derivative of the designed Lyapunov–Krasovskii functional, quadratically stable condition is established for the delayed fuzzy system in terms of linear matrix inequalities and analyse the H∞,thinmathspaceL2−L∞, passivity, mixed H∞ and passivity, false(scriptQ,scriptS,scriptRfalse)‐dissipativity execution by choosing the weighting matrices can be solved simultaneously in a standard framework based on the idea of extended dissipative. Finally, simulation studies are given to verify the effectiveness of the derived results, among them one example was supported by the real‐life application of the benchmark problem in the sense of STD signals.

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