Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates

Wu, Zheng‐Guang; Park, Ju H.; Su, Hongye; Chu, Jian

doi:10.1016/j.nonrwa.2012.02.009

Cited by 52 publications

(20 citation statements)

References 37 publications

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“…Obviously, it is not a homogeneous process. Driven by these practical problems, people turn to the nonhomogeneous Markov jump systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…The ∞ estimation problem is investigated. This assumption is generalized to the continuous-time Markov jump system [7], Markov jump neural networks [8,9], complex networks [10], and singular Markov jump systems [11], and the robust stability, stochastic stability, passivity analysis, and synchronization are studied, respectively. Another way of describing timevarying characteristics is in a polytopic sense.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis for a Class of Discrete‐Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Zhou

Chen

et al. 2018

Complexity

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This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and timevarying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis for a Class of Discrete‐Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Zhou

Chen

et al. 2018

Complexity

View full text Add to dashboard Cite

show abstract

“…The characteristic of passive properties is that they can make the systems internally stable. During the past several years, the passivity problem for time-delay systems has been investigated in the literature [16][17][18][19][20][21][22]. In [16][17][18][19][20][21][22], authors investigated the passivity of neural networks with time-varying delays and gave the corresponding criteria for checking the passivity.…”

Section: Introductionmentioning

confidence: 99%

“…During the past several years, the passivity problem for time-delay systems has been investigated in the literature [16][17][18][19][20][21][22]. In [16][17][18][19][20][21][22], authors investigated the passivity of neural networks with time-varying delays and gave the corresponding criteria for checking the passivity. It is worth noting that the passivity conditions in [16][17][18][19][20][21][22] were derived on the basis of quadratic Lyapunov-Krasovskii functional in which the involved symmetric matrix was always assumed to be positive.…”

Section: Introductionmentioning

confidence: 99%

“…In [16][17][18][19][20][21][22], authors investigated the passivity of neural networks with time-varying delays and gave the corresponding criteria for checking the passivity. It is worth noting that the passivity conditions in [16][17][18][19][20][21][22] were derived on the basis of quadratic Lyapunov-Krasovskii functional in which the involved symmetric matrix was always assumed to be positive. However, the results in [16][17][18][19][20][21][22] may still be conservative and not relaxed enough to be applied.…”

Section: Introductionmentioning

confidence: 99%

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New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays

Xiao

Zhong

2015

ISA Transactions

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Robust dissipative control for semilinear Markovian jump distributed parameter systems with time‐varying delay and incomplete transition probabilities

Song

Wang

Song

et al. 2019

Asian Journal of Control

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This paper investigates the robust stabilization problem of semilinear Markovian jump distributed parameter systems (which are modeled by parabolic partial differential equations) with time-varying delay and incomplete transition probabilities. Based on Takagi-Sugeno (T-S) fuzzy theory, a T-S fuzzy model is obtained to describe the nonlinear systems. Furthermore, by constructing a novel Lyapunov functional candidate, several sufficient delay-dependent conditions, which ensure the considered systems stochastically stable and strictly dissipative, are established in terms of linear matrix inequalities. Finally, a fuzzy controller design approach is proposed, and two examples are presented to demonstrate the effectiveness of the designed controller.

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Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates

Cited by 52 publications

References 37 publications

Stability Analysis for a Class of Discrete‐Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Stability Analysis for a Class of Discrete‐Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays

Robust dissipative control for semilinear Markovian jump distributed parameter systems with time‐varying delay and incomplete transition probabilities

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