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首页> 外文会议>Mediterranean Conference on Control and Automation >On the Finite-Region Stability of 2-D Systems
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On the Finite-Region Stability of 2-D Systems

机译：关于2-D系统的有限区稳定性

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摘要

Some recent papers have extended the concept of finite-time stability (FTS) to the context of 2-D linear systems, where it has been referred to as finite-region stability (FRS). FRS methodologies make even more sense than the classical FTS approach developed for 1-D systems, since the state variables of 2-D systems often depend on a pair of space coordinates, rather than on time, as it is the case, for instance, of the image processing framework. Since space coordinates clearly belong to finite intervals, FRS techniques are much more effective than the classical Lyapunov approach, which looks to the asymptotic behavior of the system over an infinite interval. To this regard, the novel contribution consists of a new sufficient condition for FRS of linear time-varying (LTV) discrete-time 2-D systems, which turns out to be less conservative than those ones provided in the existing literature. Then, a sufficient condition to solve the finite-region stabilization problem is proposed. All the results provided in the paper lead to optimization problems constrained by linear matrix inequalities (LMIs), that can be solved via widely available software. Numerical examples illustrate and validate the effectiveness of the proposed technique.
机译：一些最近的论文已经将有限时间稳定性（FTS）的概念扩展到2-D线性系统的背景下，其中被称为有限区域稳定性（FRS）。 FRS方法甚至比为1-D系统开发的古典FTS方法更具意义，因为2-D系统的状态变量通常依赖于一对空间坐标，而不是按时，因为它是这种情况，图像处理框架。由于空间坐标清楚地属于有限间隔，因此FRS技术比经典的Lyapunov方法更有效，这在无限间隔内对系统的渐近行为看起来更有效。为这方面，新颖的贡献包括用于线性时变（LTV）离散时间2-D系统的FRS的新的充分条件，其结果比现有文献中提供的那些较少保守。然后，提出了一种解决有限区域稳定问题的足够条件。本文中提供的所有结果都导致线性矩阵不等式（LMI）限制的优化问题，可以通过广泛的可用软件来解决。数值示例说明并验证了所提出的技术的有效性。

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