Exact null controllability, stabilizability, and detectability of linear nonautonomous control systems: a quasisemigroup approach
type: Item
instance of: scholarly article
title: Exact null controllability, stabilizability, and detectability of linear nonautonomous control systems: a quasisemigroup approach
zbMATH Open document ID: 1470.93073
DOI: 10.1155/2018/3791609
author: Sutrima
author: Ch. Rini Indrati
author: Lina Aryati
published in: Abstract and Applied Analysis
publication date: 2019-02-25T00:00:00Z
review text: Summary: In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated \(C_0\)-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 7029285
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3791609
OpenAlex ID: W2898773721
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description: scientific article; zbMATH DE number 7029285