New noise‐to‐state stability and instability criteria for random nonlinear systems

Yao, Liqiang; Zhang, Weihai

doi:10.1002/rnc.4773

Cited by 21 publications

(4 citation statements)

References 34 publications

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“…Thus, it makes sense to relax restrictions on the Lyapunov function in the stability criterion. As is shown in [33][34][35], the negativity of the time-derivative for the Lyapunov function in the stability criterion was relaxed by the uniformly asymptotically stable function (UASF). For discrete-time time-varying systems, the improved stability criteria were established in [36,37] based on the uniformly exponentially stable function (UESF) in the sense that the time-shifts in the criteria can be selected as positive values at some moment.…”

Section: Introductionmentioning

confidence: 99%

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Feng

Park

Zhang

2020

IET Control Theory & Appl

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This paper considers noise‐to‐state stability for random non‐linear systems with stochastic impulses. The impulsive random non‐linear systems contain three random characteristics: the second‐moment processes in continuous dynamics, the sequence of random variables in discrete dynamics, and the number of stochastic impulses obeyed a renewal process. Firstly, the improved criteria of noise‐to‐state stability are established for random non‐linear systems subject to unstable stochastic impulses based on the uniformly asymptotically stable function. Secondly, improved Lyapunov approaches of NSS with unstable stochastic continuous dynamics are accomplished by the uniformly exponentially stable function. Finally, two numerical examples are used to illustrate the feasibility of the proposed methods.

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Section: Introductionmentioning

confidence: 99%

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Feng

Park

Zhang

2020

IET Control Theory & Appl

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“…Zhou et al generalized this idea by establishing a uniformly asymptotically stable function (UASF) framework and proposed stability criteria for nonlinear time-varying systems, time-delay systems and time-varying stochastic time-delay systems. [20][21][22] Yao and Zhang 23 provided the noise-to-state stability and instability criteria for random nonlinear affine systems based on indefinite Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Indefinite multiple Lyapunov functions ofpth moment input‐to‐state stability andpth moment integral input‐to‐state stability for the nonlinear time‐varying stochastic systems with Markovian switching

Liu

Ning

2021

Intl J Robust & Nonlinear

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Thepth moment input‐to‐state stability and thepth moment integral input‐to‐state stability of stochastic systems with Markovian switching are investigated in this article. Sufficient conditions are provided by indefinite multiple Lyapunov functions (iMLFs) with a time‐varying sojourn time condition. These criteria quantify the stability of each individual subsystem with time‐varying infinitesimal generator of Lyapunov function, which allows infinitesimal generators to be positive in some intervals. An integral form of the sojourn time is introduced to replace the switch count process, which proposes a relaxed switching constraint. Uniformly asymptotic stability and uniformly exponential stability conditions with iMLFs are also presented. Some comparisons are given through theoretical derivations to show the advantages of the proposed results. Finally, two numerical examples verify the effectiveness and the advantages of the presented results.

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“…Taking into account this point, it is more appropriate to describe the random disturbance with a second‐order moment process, whose mean power is bounded 17,18 . For random nonlinear systems driven by a second‐order moment process, many salient results have been reported 19‐22 …”

Section: Introductionmentioning

confidence: 99%

Stability criteria of random delay differential systems subject to random impulses

Zhang

Feng

et al. 2021

Intl J Robust & Nonlinear

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This article investigates the stability of random impulsive delay differential systems with the kind of random impulsive intensity determined by an arbitrary random sequence or an irreducible aperiodic Markov chain. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second‐order moment processes. Based on the approaches of average impulsive interval and mode‐dependent average impulsive interval, the criteria of global asymptotic stability in probability and exponential stability in mth moment are constructed, respectively. In the end, the feasibility of the proposed theoretical results is verified by an example.

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New noise‐to‐state stability and instability criteria for random nonlinear systems

Cited by 21 publications

References 34 publications

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Indefinite multiple Lyapunov functions ofpth moment input‐to‐state stability andpth moment integral input‐to‐state stability for the nonlinear time‐varying stochastic systems with Markovian switching

Stability criteria of random delay differential systems subject to random impulses

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