Robust Stabilizability of linear uncertain switched systems : a computational algorithm

C. Yfoulis
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引用次数: 2

Abstract

The problem of robust stabilizability of linear uncertain systems with unstable modes has recently attracted increased interest. Given a number of unstable linear uncertain subsystems, the problem is to determine stabilizing switching sequences resulting in asymptotically stable behavior or to ascertain the absence of such laws. In a number of recent publications, necessary and sufficient conditions for the stabilizability problem have been sought. It is well known that the class of polyhedral Lyapunov functions is universal for the asymptotic stability of linear uncertain switched systems with stable subsystems. Recent results suggest that this property holds for linear uncertain switched systems with unstable subsystems, at least under some further assumptions. Motivated by these theoretical advancements, in this paper we deal with the development of a computational technique that generates polyhedral Lyapunov functions for the stabilizability problem. First, we propose an improved reliable and efficient computational algorithm for two-dimensional systems, extending the results in [11] and [14]. Second, we show how the main idea may be modified in a sufficient form to allow higher-dimensional systems to be dealt with. Further development of these computational tools for higher-dimensional systems will be the subject of future work.
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线性不确定切换系统的鲁棒稳定性:一种计算算法
具有不稳定模态的线性不确定系统的鲁棒稳定性问题近年来引起了人们越来越多的关注。给定一些不稳定的线性不确定子系统,问题是确定导致渐近稳定行为的稳定切换序列或确定不存在这种律。在最近的一些出版物中,已经寻求了稳定性问题的充分必要条件。对于具有稳定子系统的线性不确定切换系统的渐近稳定性,多面体李雅普诺夫函数是通用性的。最近的结果表明,至少在一些进一步的假设下,这个性质对于具有不稳定子系统的线性不确定切换系统是成立的。在这些理论进步的激励下,在本文中,我们讨论了为稳定性问题生成多面体李雅普诺夫函数的计算技术的发展。首先,我们提出了一种改进的二维系统可靠高效的计算算法,扩展了文献[11]和[14]的结果。其次,我们展示了如何以足够的形式修改主要思想,以允许处理更高维度的系统。这些计算工具在高维系统中的进一步发展将是未来工作的主题。
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