9 research outputs found
An LMI Condition for the Robustness of Constant-Delay Linear Predictor Feedback with Respect to Uncertain Time-Varying Input Delays
This paper discusses the robustness of the constant-delay predictor feedback
in the case of an uncertain time-varying input delay. Specifically, we study
the stability of the closed-loop system when the predictor feedback is designed
based on the knowledge of the nominal value of the time-varying delay. By
resorting to an adequate Lyapunov-Krasovskii functional, we derive an LMI-based
sufficient condition ensuring the exponential stability of the closed-loop
system for small enough variations of the time-varying delay around its nominal
value. These results are extended to the feedback stabilization of a class of
diagonal infinite-dimensional boundary control systems in the presence of a
time-varying delay in the boundary control input.Comment: Published in Automatica as a brief pape
Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems with Delay Boundary Control
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.Comment: Preprin
ISS Property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems
This paper deals with the establishment of Input-to-State Stability (ISS) estimates for infinite dimen-sional systems with respect to both boundary and distributed disturbances. First, a new approach isdeveloped for the establishment of ISS estimates for a class of Riesz-spectral boundary control systemssatisfying certain eigenvalue constraints. Second, a concept of weak solutions is introduced in order torelax the disturbances regularity assumptions required to ensure the existence of classical solutions.The proposed concept of weak solutions, that applies to a large class of boundary control systemswhich is not limited to the Riesz-spectral ones, provides a natural extension of the concept of bothclassical and mild solutions. Assuming that an ISS estimate holds true for classical solutions, we showthe existence, the uniqueness, and the ISS property of the weak solutions.European Commission - European Regional Development FundScience Foundation IrelandPreprint so no embargo - A
ISS Property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems
This paper deals with the establishment of Input-to-State Stability (ISS) estimates for infinite dimen-sional systems with respect to both boundary and distributed disturbances. First, a new approach isdeveloped for the establishment of ISS estimates for a class of Riesz-spectral boundary control systemssatisfying certain eigenvalue constraints. Second, a concept of weak solutions is introduced in order torelax the disturbances regularity assumptions required to ensure the existence of classical solutions.The proposed concept of weak solutions, that applies to a large class of boundary control systemswhich is not limited to the Riesz-spectral ones, provides a natural extension of the concept of bothclassical and mild solutions. Assuming that an ISS estimate holds true for classical solutions, we showthe existence, the uniqueness, and the ISS property of the weak solutions.European Commission - European Regional Development FundScience Foundation IrelandPreprint so no embargo - A