Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems with Delay Boundary Control
For control theorists, this provides a rigorous stabilization method for a class of infinite-dimensional systems with delay, though it is incremental due to reliance on existing techniques like Artstein transformation and pole-shifting.
This paper addresses boundary feedback stabilization of diagonal infinite-dimensional systems with delayed boundary control. The proposed method stabilizes the system using a finite-dimensional delay controller, achieving exponential Input-to-State Stability (ISS) and a small-gain condition for IDS-ODE interconnections.
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.