Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-12T21:28:59.703Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability enhancement of output for a class of linear parabolic systems

Published online by Cambridge University Press:  12 July 2007

Takao Nambu
Takao Nambu
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Kobe University, Nada, Kobe 657-8501, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

In regular state stabilization of a class of linear parabolic systems, the number of the sensors wk and the actuators hk are required to be greater than or equal to the maximum of the multiplicities of the unstable eigenvalues. In this paper, we ask what control theoretic results we can establish with smaller numbers of wk and hk. The enhancement of stability of output or the output stabilization, a concept weaker than regular state stabilization, gives an answer to the question. Conditions of a fairly different nature than those for regular state stabilization appear; these are the rank conditions of the products of the observability and controllability matrices. The result is applied to a parabolic system with boundary observation/control via two different approaches.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 1 , February 2003 , pp. 157 - 175
Copyright
Copyright © Royal Society of Edinburgh 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)