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首页> 外文期刊>Automatic Control, IEEE Transactions on >Uniform Stabilization of Nonlinear Systems With Arbitrary Switchings and Dynamic Uncertainties
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Uniform Stabilization of Nonlinear Systems With Arbitrary Switchings and Dynamic Uncertainties

机译：具有任意切换和动态不确定性的非线性系统的一致镇定

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摘要

We solve the problem of global uniform input-to-state stabilization of nonlinear switched systems with time-varying and periodic dynamics, with dynamic uncertainties, and with external disturbances. The switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form (GTF) with non-invertible input-output maps. In our first and most general result, we prove that, if the dynamic uncertainty is treated as external disturbance, then the general triangular form system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty by means of a switching-independent, smooth and periodic feedback. Hence, using a suitable extension of the well-known small gain theorem to our case of switched systems with arbitrary switchings, we obtain the uniform input-to-state stabilization of the entire interconnected system. The second part of the paper addresses a more special case of triangular form (TF) switched systems with right-invertible input-output (I-O) maps with unknown switchings and with dynamic uncertainties. We show that the design becomes simpler and more constructive and the controllers become time-invariant if the dynamics is autonomous in this special case. Finally, we consider an example with explicit design of the stabilizing controllers.
机译：我们解决了具有时变和周期动态，动态不确定性和外部干扰的非线性切换系统的全局一致输入到状态稳定的问题。假设开关信号未知，并且状态向量的已知分量的动态等效于具有不可逆输入输出映射的一般三角形式（GTF）。在我们的第一个也是最普遍的结果中，我们证明了，如果将动态不确定性视为外部干扰，则可以用任意小的增益w.r.t稳定一般的三角形式的系统。通过与开关无关，平稳且周期性的反馈来确定动态不确定性。因此，使用众所周知的小增益定理的适当扩展到具有任意切换的切换系统的情况下，我们可以获得整个互连系统的统一输入到状态稳定度。本文的第二部分介绍了三角形式（TF）交换系统的一种更特殊的情况，该系统具有右反转的输入输出（I-O）映射，具有未知的开关且具有动态不确定性。我们表明，在这种特殊情况下，如果动力学是自主的，则设计将变得更简单，更具建设性，并且控制器将变得时不变。最后，我们以稳定控制器的显式设计为例。

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