Stabilizability and Existence of System Representations for Discrete-Time Time-Varying Systems
Stabilizability and Existence of System Representations for Discrete-Time Time-Varying Systems
复制标题
DOI：
10.23919/acc.1991.4791900
复制
发表时间：
1991-06
期刊：
影响因子：
--
通讯作者：
W. N. Dale;Malcolm C. Smith
中科院分区：
文献类型：
--
作者：
W. N. Dale;Malcolm C. Smith
在本文中，我们开发了右和左表示作为一种替代，但等价的，框架互质因子分解的运营商。本文的主要定理建立了一个线性、时变、离散时间对象是可镇定的当且仅当它的图可以表示为值域（分别为核）的因果，有界算子是左（分别）。右）可逆的。证明依赖于某些因式分解定理的Arveson套代数。本文将所有稳定补偿器的Youla参数化扩展到这个框架中，并考虑了Feintuch的时变工厂的一个例子，并证明了它是不可稳定的。最后，连续时间的情况下进行检查，并讨论了在扩展我们的证明遇到的问题。然而，我们能够证明，一个稳定的植物必须有一个封闭的图形，我们用这个来证明一个例子的时不变，连续时间系统的Shefi是不稳定的。
In this paper, we develop right and left representations as an alternate, but equivalent, framework to coprime factorizations of operators. The main theorem of the paper establishes that a linear, time-varying, discrete-time plant is stabilizable if and only if its graph can be represented as the range (resp. kernel) of a causal, bounded operator which is left (resp. right) invertible. The proof relies on certain factorization theorems of Arveson for nest algebras. The paper extends the Youla parametrization of all stabilizing compensators to this framework and an example of a time-varying plant of Feintuch is considered and shown to be not stabilizable. Finally, the continuous-time case is examined and the problems encountered in extending our proof are discussed. However, we are able to prove that a stabilizable plant must have a closed graph and we use this to prove that an example of a time-invariant, continuous-time system of Shefi is not stabilizable.