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首页> 外文期刊>IFAC PapersOnLine >Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations
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Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations

机译：离散时间线性切换系统的镇定：Lyapunov-Metzler不等式与S过程表征

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In this paper we study connections between Lyapunov-Metzler inequalities and S-procedure characterizations in the context of stabilizing discrete-time switched linear systems using min-switching strategies. We propose two generalized versions of S-procedure characterization along the lines of the generalized versions of Lyapunov-Metzler inequalities recently proposed in the literature. It is shown that the existence of a solution to the generalized version(s) of Lyapunov-Metzler inequalities is equivalent to the existence of a solution to the generalized version(s) of S-procedure characterization with a restricted choice of the scalar quantities involved in the latter. This recovers some of our earlier works on the classical Lyapunov-Metzler inequalities as a special case. We also highlight and discuss an open question of whether the generalized versions of S-procedure characterization are strictly less conservative than the generalized versions of Lyapunov-Metzler inequalities, which in turn are equivalent to periodic stabilizability as was recently shown.
机译：在本文中，我们研究了在使用最小切换策略稳定离散时间切换线性系统的情况下，Lyapunov-Metzler不等式与S过程表征之间的联系。我们根据文献中最近提出的Lyapunov-Metzler不等式的广义版本，提出了S过程表征的两个广义版本。结果表明，对Lyapunov-Metzler不等式的广义版本的解的存在等同于对S过程表征的广义版本的解的存在，其中所涉及的标量的选择受到限制在后者。作为特殊情况，这可以恢复我们先前有关经典Lyapunov-Metzler不等式的一些著作。我们还强调并讨论了一个开放性问题，即S过程表征的广义版本是否严格不如Lyapunov-Metzler不等式的广义版本保守，后者又等效于周期性稳定性，如最近所示。

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