A Condition for Almost Global Stability and Local Asymptotical Stability of Nonlinear System

机译：几乎全球稳定性和非线性系统局部渐近稳定性的条件

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For nonlinear autonomous systems with the origin as a fixed point, the existence of a density function with its time derivative greater than zero implies almost global stability and local asymptotical stability, which is convenient for verification. Further, if the divergence at the origin is less than zero, the existence of a density function with its time derivative greater than zero is both necessary and sufficient condition for almost global stability and local asymptotical stability. Examples illustrate the validity of the results.

机译：对于具有固定点的非线性自治系统，其时间衍生物大于零的密度函数的存在意味着几乎是全局稳定性和局部渐近稳定性，这方便验证。此外，如果原点的发散小于零，则具有大于零的时间衍生物的密度函数的存在是必要的，并且对于几乎全局稳定性和局部渐近稳定性。示例说明了结果的有效性。

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《International Workshop on Information and Electronics Engineering》|2013年||共5页
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作者
Jiafeng Yu; Jian Wang; Qinsheng Li;
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中图分类无线通信;
关键词
density functions; almost global stability; nonlinear systems; local asymptotical stability; convergence criterion;

机译：密度函数;几乎全局稳定;非线性系统;局部渐近稳定性;收敛标准;

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1. LMI CONDITION FOR GLOBAL ASYMPTOTIC STABILITY OF 2-D DISCRETE UNCERTAIN STATE-DELAYED SYSTEMS WITH GENERALIZED OVERFLOW NONLINEARITIES [J] . A. Dey, H. Kar The Mediterranean Journal of Measurement and Control . 2012,第1期

机译：具有广义溢出非线性的二维离散不确定状态时滞系统的全局渐近稳定性的LMI条件
2. DELAY-DEPENDENT LMI CONDITION FOR GLOBAL ASYMPTOTIC STABILITY OF DISCRETE-TIME SYSTEMS WITH TIME-VARYING DELAY SUBJECT TO PARTIAL STATE SATURATION NONLINEARITIES [J] . P. Kokil, V. K. R. Kandanvli, H. Kar The Mediterranean Journal of Measurement and Control . 2012,第4期

机译：具部分状态饱和非线性的时滞离散系统的全局渐近稳定性的时滞相关LMI条件
3. Delay-dependent LMI condition for global asymptotic stability of discrete-time uncertain state-delayed systems using quantization/overflow nonlinearities [J] . Kandanvli V.K.R., Kar H. International Journal of Robust and Nonlinear Control . 2011,第14期

机译：基于量化/溢出非线性的离散时间不确定状态滞后系统的全局渐近稳定性的时滞相关LMI条件
4. A Condition for Almost Global Stability and Local Asymptotical Stability of Nonlinear System [C] . Jiafeng Yu, Jian Wang, Qinsheng Li International Workshop on Information and Electronics Engineering . 2013

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5. Necessary and sufficient conditions for global asymptotic stability of third-order conewise linear systems [D] . Shokralla, Shaddy Samir Zaki 2006

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6. An LMI Based Criterion for Global Asymptotic Stability of Discrete-Time State-Delayed Systems with Saturation Nonlinearities [O] . Priyanka Kokil 2014

机译：具有饱和非线性的离散状态时滞系统的全局渐近稳定性的基于LMI的准则
7. A Condition for Almost Global Stability and Local Asymptotical Stability of Nonlinear System [O] . Yu Jiafeng, Wang Jian, Li Qinsheng 2012

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8. Conditions for Global Stability of Two Linearly Interconnected Nonlinear Systems. [R] . McClamroch, N. H., Ianculescu, G. D. 1974

机译：两个线性互联非线性系统的全局稳定性条件。

A Condition for Almost Global Stability and Local Asymptotical Stability of Nonlinear System

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