Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem
Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem
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无限维系统的内部和外部稳定性之间的关系及其在伺服问题中的应用
DOI：
10.1109/9.14416
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
S. Hara
中科院分区：
文献类型：
--
作者：
Y. Yamamoto;S. Hara
本文研究了一类无限维系统的各种稳定性概念之间的关系，其中包含现有方法未涵盖的一类系统，例如具有无限多个不稳定极点的系统。证明了i)内部L2稳定性和指数稳定性是等价的； ii) 内部稳定性意味着H¿-稳定性。推导了内部稳定的几个必要条件和充分条件。特别是，证明了在某些条件下，如果一个规范实现是外部稳定的，那么它就是内部稳定的。这些结果适用于涉及此类系统的伺服问题。结果表明，i) 内部模型对于跟踪是必要的； ii) 内部模型以及闭环稳定性意味着跟踪。讨论了一个称为重复控制系统的典型示例来说明结果。
This paper studies the relationships among various stability notions for a class of infinite-dimensional systems, which contains a class of systems not covered by the existing method, e.g., those having infinitely many unstable poles. It is proved thai i) internal L2-stability and exponential stability are equivalent; ii) internal stability implies H¿-stability. Several necessary conditions and sufficient conditions for internal stability are derived. In particular, it is proved that, under certain conditions, a canonical realization is internally stable if it is externally stable. These results are applied to the servo problem involving this class of systems. It is shown that i) an internal model is necessary for tracking; ii) an internal model along with closed-loop stability implies tracking. A typical example, called a repetitive control system, is discussed to illustrate the results.