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A-Stability and Stochastic Mean-Square Stability

BIT Numerical Mathematics, 2000
The author considers the mean-square stability of the stochastic differential equation for the test problem with multiplicative noise proposed by \textit{Y. Saito} and \textit{T. Mitsui} [SIAM J. Appl. Math. 56, No. 5, 1400-1423 (1996; Zbl 0869.60053)]. It quantifies precisely the point where unconditional stability is lost.
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Mean square stability for Markov jump Boolean networks

Science China Information Sciences, 2019
In this paper, one of the stability definitions of Markov jump Boolean networks (MJBNs), called mean square stability (MSS), is investigated.Some necessary and sufficient conditions are presented to guarantee the MSS of such MJBNs. Moreover, one of the necessary and sufficient conditions for MSS is obtained in terms of linear programming, which implies
Liqing Wang, Mei Fang, Zheng-Guang Wu
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Mean square exponential stability

2009
The problem of mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. Four different definitions of the concept of exponential stability in the mean square are introduced and it is shown that they are not always equivalent.
Vasile Drăgan   +2 more
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Mean square stabilization for stochastic switched fuzzy systems

2016 Chinese Control and Decision Conference (CCDC), 2016
In this paper, a mean square stabilization criterion for stochastic switched fuzzy (SSF) systems is proposed. SSF system, which differs from existing ones, can often incorporate discrete states, continuous dynamics and randomness as well as their interactions in complex real-world systems.
Hong Yang   +5 more
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Exponential Stability in Mean Square

2013
In this chapter the problem of mean square exponential stability of the zero solution to the stochastic differential equations of type (1.22) is studied. The stability of a steady-state is one of the main tasks which appears in many design problems of controllers with prescribed performances.
Vasile Dragan   +2 more
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Mean-square exponential stability of stochastic inertial neural networks

International Journal of Control, 2020
By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments.
Wentao Wang, Wei Chen
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Mean square exponential stabilization of sampled‐data Markovian jump systems

International Journal of Robust and Nonlinear Control, 2018
SummaryIn this paper, the problem of mean square exponential stabilization for sampled‐data Markovin jump systems is studied. A time‐scheduled Lyapunov functional consisting of a exponential‐type looped function is constructed using segmentation technology and linear interpolation.
Guoliang Chen, Jian Sun, Jie Chen
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Mean square exponential stability of stochastic nonlinear delay systems

International Journal of Control, 2016
ABSTRACTIn this paper, we are concerned with the stability of stochastic nonlinear delay systems. Different from the previous literature, we aim to show that when the determinate nonlinear delay system is globally exponentially stable, the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable.
Quanxin Zhu, Shiyun Song, Tianren Tang
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Mean square stability conditions for discrete stochastic bilinear systems

IEEE Transactions on Automatic Control, 1985
The paper considers first and second order stability properties of discrete-time stochastic (bi-) linear systems of the form \[ x(i+1)=[A_ 0+\sum^{p}_{k=1}w_ k(i) A_ k]x(i)+Bu(i)\quad in\quad {\mathbb{C}}^ n, \] where \(A_ 0,...,A_ p\) are complex matrices of appropriate dimension, and \(\{\) (w(i), u(i)), \(i\geq 0\}\) is an independent second order ...
Kubrusly, C. S., Costa, O. L. V.
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Mean square stability criteria for stochastic feedback systems

International Journal of Systems Science, 1973
Abstract In this paper several stability criteria are obtained for a class of stochastic feedback systems containing a multiplicative white noise element ; continuous time as well as discrete time systems are dealt with. Mean square stability properties are derived by means of Lyapunov theory ; the Lyapunov functions are generated by means of the ...
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