Quadratic stabilization and L2 gain analysis of switched affine systems
Quadratic stabilization and L2 gain analysis of switched affine systems
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DOI：
10.1109/ccdc.2017.7978848
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发表时间：
2017-07
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影响因子：
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通讯作者：
Chi Huang;G. Zhai;Wenzhi Li
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文献类型：
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作者：
Chi Huang;G. Zhai;Wenzhi Li
我们考虑由一组有限的时不变仿射子系统组成的切换系统的二次稳定和 L2 增益分析。子系统矩阵和向量都被切换，并且没有一个子系统具有所需的二次稳定性或特定的 L2 增益属性。我们证明，如果子系统矩阵的凸组合是 Hurwitz，而仿射向量的另一个凸组合为零，那么我们可以设计一个状态相关的切换律（状态反馈）和一个输出相关的切换律（输出反馈），使得整个切换系统是二次稳定的。该结果也推广到状态反馈下的L2增益分析。
We consider quadratic stabilization and L2 gain analysis for switched systems which are composed of a finite set of time-invariant affine subsystems. Both subsystem matrices and vectors are switched, and no single subsystem has desired quadratic stability or specific L2 gain property. We show that if a convex combination of subsystem matrices is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched system is quadratically stable. The result is also extended to L2 gain analysis under state feedback.