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首页> 外文期刊>IEEE Transactions on Automatic Control >Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions
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Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions

机译：通过二次和非二次Lyapunov函数的饱和系统的稳定性和性能

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摘要

In this paper, we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration. The only assumptions we make about the system are well-posedness of the algebraic loop and local stability. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of bounded energy disturbances and the nonlinear L2 gain. The regional analysis is established through an effective treatment of the algebraic loop and the saturation/deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Adjustable parameters are incorporated into the differential inclusions to reflect the regional property. The main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain Lyapunov function where the PDI or the NDI is valid. With quadratic Lyapunov functions, conditions for stability and performances are derived as linear matrix inequalities (LMIs). To obtain less conservative conditions, we use a pair of conjugate non-quadratic Lyapunov functions, the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the corresponding LMI conditions as special cases, hence the BMI results are guaranteed to be as good as the LMI results. In most examples, the BMI results are significantly better than the LMI results
机译：在本文中，我们开发了一种系统的Lyapunov方法，用于在一般反馈配置下对饱和系统的区域稳定性和性能进行分析。我们对系统所做的唯一假设是代数环的适定性和局部稳定性。要考虑的问题包括吸引域的估计，在一类有界能量扰动下的可达集以及非线性L2增益。通过有效处理代数环和饱和度/死区功能来建立区域分析。此处理产生两种形式的差异包含物，即包含原始系统的多位差异包含物（PDI）和有界约束的差异包含物（NDI）。可调参数被纳入微分包含物中以反映区域属性。区域分析的主要思想是确保状态保持在PDI或NDI有效的某个Lyapunov函数的水平集中。使用二次Lyapunov函数，可以将稳定性和性能条件导出为线性矩阵不等式（LMI）。为了获得较少的保守条件，我们使用一对共轭非二次Lyapunov函数，凸包二次函数和最大二次函数。这些函数产生双线性矩阵不等式（BMI），作为稳定性和保证的性能水平的条件。 BMI条件涵盖了特殊情况下对应的LMI条件，因此可以保证BMI结果与LMI结果一样好。在大多数示例中，BMI结果明显优于LMI结果

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