Novel<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math>state estimation of static neural networks with interval time-varying delays via augmented Lyapunov–Krasovskii functional

Ali, M. Syed; Saravanakumar, Ramasamy; Arik, Sabri

doi:10.1016/j.neucom.2015.07.038

Cited by 32 publications

(3 citation statements)

References 28 publications

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“…If holds a feasible solution, then the gain matrix L is given by

L = P_{2}^{prefix- 1} R^{T}

.Remark In this paper, we assume that the delay is known and bounded. In , observer design was investigated for systems with time delay that is known and bounded. However, to the best of our knowledge, few results have been obtained on the study of observers for nonlinear systems with unknown time‐varying delay with a known bound.…”

Section: Resultsmentioning

confidence: 99%

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

Dong

Liu

Liang

2016

Intl J Robust & Nonlinear

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SUMMARYThis paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time-varying delay and the one-sided Lipschitz condition. By constructing the novel Lyapunov-Krasovskii functional while utilizing the free-weighting matrices approach, the one-sided Lipschitz condition and the quadratic inner-bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time-varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method.

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“…If holds a feasible solution, then the gain matrix L is given by

L = P_{2}^{prefix- 1} R^{T}

Section: Resultsmentioning

confidence: 99%

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

Dong

Liu

Liang

2016

Intl J Robust & Nonlinear

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“…However, these results were restricted to filtering problems based on H ∞ performance. Thus, this paper can be combined with the results presented in [38], [40], [41], [43], and [46] to produce new results on exponential dissipative and l 2 -l ∞ filter design for DSNNs. Remark 8: Recently, a new free-matrix-based integral inequality was proposed by Zeng et al [55], [56] to further reduced the potential conservatism of conditions.…”

Section: Exponential L 2 -L ∞ Filter Designmentioning

confidence: 95%

“…Our findings can be integrated with these studies to produce new results. In [38], [40], [41], [43], and [46], filter design methods were introduced for NNs by constructing suitable Lyapunov-Krasovskii functionals. However, these results were restricted to filtering problems based on H ∞ performance.…”

Section: Exponential L 2 -L ∞ Filter Designmentioning

confidence: 99%

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ – $l_{\infty }$ Performances

Choi

Ahn

Karimi

et al. 2017

IEEE Trans. Cybern.

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This paper studies delay-dependent exponential dissipative and l - l filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l - l senses. The design of the desired exponential dissipative and l - l filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

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Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

Tan

Dian

Zhao

2017

Asian Journal of Control

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This paper discusses the issue of stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing an appropriate augmented fuzzy Lyapunov-Krasovskii functional (LKF) including non-quadratic Lyapunov matrices and triple and quadruple integral term,less conservative and newer stability conditions are introduced. In order to obtain stability conditions in the form of linear matrix inequalities (LMIs), some tighter bounding inequalities are employed to estimate the derivative of LKF. Several examples are provided to illustrate the effectiveness of the suggested approaches.

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NovelH∞state estimation of static neural networks with interval time-varying delays via augmented Lyapunov–Krasovskii functional

Cited by 32 publications

References 28 publications

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ – $l_{\infty }$ Performances

Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

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