Adding Integral Action for Open-Loop Exponentially Stable Semigroups and Application to Boundary Control of PDE Systems

The article deals with the output feedback regulation of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic partial differential equation (PDE) systems and an example of...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2020-11, Vol.65 (11), p.4481-4492
Main Authors: Terrand-Jeanne, Alexandre, Andrieu, Vincent, Martins, Valerie Dos Santos, Xu, Cheng-Zhong
Format: Article
Language:English
Subjects:
Analysis of PDEs
Automatic
Boundary control
Closed loop systems
Control stability
Control theory
Distributed parameter systems
Engineering Sciences
Feedback control
Hilbert space
Hyperbolic systems
Integral equations
Integrals
Lyapunov methods
Mathematics
Output feedback
output feedback regulation
Parabolic differential equations
Partial differential equations
PI control
Robustness
Stability
Xenon
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Summary:The article deals with the output feedback regulation of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic partial differential equation (PDE) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The proof is based on a novel Lyapunov functional construction that employs the forwarding techniques.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2957349