Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations
Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations
复制标题
具有反对称逐步配置的线性不确定延迟系统的稳定性
DOI：
10.1007/s10883-007-9035-3
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
H. Fujii
中科院分区：
文献类型：
--
作者：
T. Hashimoto;T. Amemiya;H. Fujii
研究了一类线性不确定时滞系统的线性无记忆状态反馈镇定问题。所考虑的每个不确定参数和每个延迟都可以在任意大的范围内随时间变化。在这种情况下，不确定元素在系统矩阵中的位置起着重要的作用。Wei提出了反对称逐步配置（ASC）的概念，并证明了具有这种配置是线性不确定系统在线性状态反馈控制下二次可镇定的充要条件。然而，他的方法是不适用于系统中包含的状态变量的延迟。另一方面，Amemiya开发的线性不确定系统的状态时滞使用线性无记忆状态反馈控制的稳定条件。本文介绍了发展的条件，这个问题已经获得了日期。从根本上证明了存在自适应控制器也是线性不确定时滞系统镇定的充分条件。对于满足可镇定性条件的系统，给出了一个简单的控制器设计方法，并举例说明。
This paper investigates the problem of designing a linear memoryless state feedback control to stabilize a class of linear uncertain systems with state delays. Each uncertain parameter and each delay under consideration might vary with time in an arbitrarily large range. In such a situation, the locations of uncertain elements in the system matrices play an important role. Wei introduced the concept of antisymmetric stepwise configuration (ASC) and proved that it is a necessary and sufficient condition for linear uncertain systems to be quadratically stabilizable using linear state feedback control to have this configuration. However, his method is inapplicable to systems that contain delays in the state variables. On the other hand, Amemiya developed conditions for the stabilization of linear uncertain systems with state delays using linear memoryless state feedback control. This paper presents development of the conditions of this problem that have been obtained to date. Fundamentally, it is proved that having an ASC is also a sufficient condition for the stabilization of linear uncertain delay systems. For systems satisfying the stabilizability conditions, a simple control design procedure is also provided and illustrated by an example.