A convex reformulation of the controller synthesis problem for MIMO single-delay systems with implementation in SOS
A convex reformulation of the controller synthesis problem for MIMO single-delay systems with implementation in SOS
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DOI：
10.23919/acc.2017.7963750
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发表时间：
2017-05
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通讯作者：
M. Peet
中科院分区：
文献类型：
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作者：
M. Peet
在本文中，我们提出了一个新的MIMO单时滞系统的稳定性条件，这是基于一个Lyapunov-Krasovskii泛函的隐式存在，但没有显式地构造这样一个功能的对偶类。这种新型的稳定性条件允许控制器的综合问题，制定为一个凸优化问题，很少或没有保守性，使用变量变换。此外，我们展示了如何反转这个变量变换，以获得稳定控制器。的稳定性和控制器的合成条件，然后使用SOS框架，利用在这一领域的最新进展。数值试验表明，无论是在“双重”稳定性测试或控制器综合条件下，几乎没有保守性。
In this paper, we propose a new dual class of stability condition for MIMO single-delay systems which is based on the implicit existence of a Lyapunov-Krasovskii functional but does not explicitly construct such a functional. This new type of stability condition allows the controller synthesis problem to be formulated as a convex optimization problem with little or no conservatism using a variable transformation. Furthermore, we show how to invert this variable transformation in order to obtain the stabilizing controller. The stability and controller synthesis conditions are then enforced using the SOS framework exploiting recent advances in this field. Numerical testing verifies there is little to no conservatism in either the “dual” stability test or the controller synthesis condition.