Paper Info
Title
Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control
Abstract
This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinite-dimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.
Year
DOI
Venue
2019
10.1109/TAC.2020.2975003
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Distributed parameter systems,delay boundary control,Lyapunov function,partial differential equation (PDE)-ordinary differential equation (ODE) interconnection
Journal
66
Issue
ISSN
Citations 
1
0018-9286
2
PageRank 
References 
Authors
0.37
9
2
Name
Order
Citations
PageRank
Lhachemi, H.1228.90
Christophe Prieur21037129.96