Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems with Delay Boundary Control

Abstract

This paper 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 in 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 infinite-dimensional system 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 infinite-dimensional system; 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.

Preprint

References in corpus (1)

• Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control

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• Nonlinear Boundary Output Feedback Stabilization of Reaction-Diffusion Equations
• Stability analysis of reaction-diffusion PDEs coupled at the boundaries with an ODE