Robust Boundary Output-Feedback Control of a Reaction-Diffusion Equation with In-Domain Disturbances
针对一类受域内扰动的反应扩散方程，设计了有限维动态输出反馈控制器，保证闭环指数稳定和输入输出稳定，并给出显式增益估计。
Abstract Output feedback control design for a class of reaction-diffusion equations with Dirichlet anti-collocated sensing and actuation subject to in-domain disturbances is addressed. Within this setting, we design a finite-dimensional dynamic output feedback controller ensuring closed-loop exponential stability and input-output stability with an explicit estimate of the input-output gain. The approach is based on the spectral decomposition of the open-loop infinite-dimensional system and on the use of a suitable Lyapunov functional candidate. Sufficient conditions in the form of matrix inequalities are given to ensure closed-loop stability. These conditions are shown to be always feasible and are employed to devise an optimal controller design algorithm based on the solutions to some linear matrix inequalities.