Stability and Performance Analysis of Nonlinear and Non-Normal Systems using Quadratic Constraints
Stability and Performance Analysis of Nonlinear and Non-Normal Systems using Quadratic Constraints
复制标题
使用二次约束的非线性和非正态系统的稳定性和性能分析
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Maziar S. Hemati
中科院分区：
文献类型：
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作者：
Aniketh Kalur;P. Seiler;Maziar S. Hemati
提出了一种分析非线性流体流动系统稳定性和暂态能量增长性能的系统论方法。所考虑的系统是由具有静态和无损非线性的反馈中的非正规线性元件组成的--NavierStokes方程是一个特例。具体地说，我们证明了非线性元件的输入输出特性可以用一组二次约束来表示。因此，可以通过求解线性系统的Lyapunov不等式来分析非线性系统，该线性系统具有一组捕捉非线性行为的二次约束。在这里，我们研究了所提出的关于Waleffe-Kim-Hamilton模型的分析框架--一个低维的过渡流和湍流剪切流的力学模型。我们提出的分析框架可以分析非线性系统给定平衡点的全局稳定性和局部稳定性。结果表明，非线性流动相互作用对系统的响应有不稳定的影响。建议分析中的拉格朗日乘子提供了关于主要的非线性流动相互作用项的附加信息。
Wepropose a system-theoretic approach for analyzing stability and transient energy growth performance of nonlinear fluid flow systems. The systems in consideration are composed of a non-normal linear element in feedback with a static and lossless nonlinearity—the NavierStokes equations being a special case. Specifically, we show that the input-output properties of the nonlinear element can be represented by a set of quadratic constraints. As a result, the nonlinear system can be analyzed by solving the Lyapunov inequalities of a linear system with a set of quadratic constraints that capture nonlinear behavior. Here, we investigate the proposed analysis framework on the Waleffe-Kim-Hamilton model—a low-dimensional mechanistic model of transitional and turbulent shear flows. Our proposed analysis framework can analyze global and local stability of a given equilibrium point of the nonlinear system. We show that nonlinear flow interactions have a destabilizing effect on the system response. The Lagrange multipliers in the proposed analysis provide additional information regarding the dominant nonlinear flow interaction terms.