Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations
Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations
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DOI：
10.1016/j.automatica.2012.10.002
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
H. Haimovich;M. Seron
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文献类型：
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作者：
H. Haimovich;M. Seron
我们提出了一种新的方法来计算一类具有可能非线性依赖于时滞状态的摄动界的切换连续时间线性系统的分量暂态界、分量终极界和不变区域。这种方法的主要优点是它的分量性质，即它允许扰动向量的每个分量有一个独立的界，并且所得到的界和集合也是分量的。这种分量方法不使用范数来界定扰动或状态向量，避免了为了获得有用的结果而对不同的状态向量分量进行缩放的需要，并且在某些情况下还可能降低保守性。本文是作者以前结果的基础上，推广到具有时滞状态依赖摄动的切换系统。从这个意义上讲，本文的贡献有三个方面：前述推广的推导；所提出的方法可以应用到的切换线性系统类与允许公共二次Lyapunov函数的切换系统之间的精确关系(这个问题在我们以前的工作中是悬而未决的)；以及推导出一种计算由状态向量分量的绝对值的仿射函数有界的切换线性系统的公共二次Lyapunov函数的方法。在后一种情况下，我们还展示了如何将我们的组件式方法与标准技术相结合，以得出可能比单独应用的任何一种方法所对应的界限更紧的界限。
We present a novel method to compute componentwise transient bounds, componentwise ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The main advantage of the method is its componentwise nature, i.e. the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise. This componentwise method does not employ a norm for bounding either the perturbation or state vectors, avoids the need for scaling the different state vector components in order to obtain useful results, and may also reduce conservativeness in some cases. The present paper builds upon and extends to switching systems with delayed-state-dependent perturbations previous results by the authors. In this sense, the contribution is three-fold: the derivation of the aforementioned extension; the elucidation of the precise relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic Lyapunov function (a question that was left open in our previous work); and the derivation of a technique to compute a common quadratic Lyapunov function for switching linear systems with perturbations bounded componentwise by affine functions of the absolute value of the state vector components. In this latter case, we also show how our componentwise method can be combined with standard techniques in order to derive bounds possibly tighter than those corresponding to either method applied individually.