Local stabilization of an unstable parabolic equation via saturated controls

Abstract

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations.

References in corpus (3)

• Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control
• Disturbance-to-State Stabilization and Quantized Control for Linear Hyperbolic Systems
• On ISS-Lyapunov functions for infinite-dimensional linear control systems subject to saturations

Cited by in corpus (4)

• Predictor-Based Output Feedback Stabilization of an Input Delayed Parabolic PDE with Boundary Measurement
• Boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and state-delay
• Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation
• Nonlinear Boundary Output Feedback Stabilization of Reaction-Diffusion Equations