Composite quadratic Lyapunov functions for constrained control systems
Composite quadratic Lyapunov functions for constrained control systems
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DOI：
10.1109/cdc.2002.1184417
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发表时间：
2002-12
期刊：
影响因子：
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通讯作者：
T. Hu;Zongli Lin
中科院分区：
文献类型：
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作者：
T. Hu;Zongli Lin
基于一组二次函数的复合二次函数已在前面的文章中被引入。揭示了该Lyapunov函数的一些重要性质。证明了该函数是连续可微的，其水平集是一组椭球的凸包。在本文中，我们利用这些结果来研究具有输入和状态约束的线性系统的集不变性。证明了对于给定的饱和线性反馈系统，一组不变椭球的凸壳也是不变的。如果一个群中的每个椭球体都可以通过饱和执行器的有界控制而保持不变，那么它们的凸壳也可以由同一个执行器保持不变。对于一组椭球，每个椭球在单独的饱和线性反馈下不变，我们还给出了一种构造使其凸壳不变的非线性连续反馈律的方法。
The composite quadratic function based on a group of quadratic functions was introduced in our earlier paper. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the convex hull of a group of ellipsoids. In this paper, we use these results to study the set invariance properties of linear systems with input and state constraints. We show that for a system under a given saturated linear feedback, the convex hull of a group of invariant ellipsoids is also invariant. If each ellipsoid in a group can be made invariant with a bounded control of the saturating actuator, then their convex hull can also be made invariant by the same actuator. For a group of ellipsoids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant.