A generalized exponential stabilization for a class of semilinear parabolic equations: Linear boundary feedback control approach

Abstract

This paper investigates the generalized exponential stabilization (GES) of a class of semilinear parabolic equations, which is a generalization of the result of exponential stabilization and has the character of accelerating decay process locally. From the point of admissibility of unbounded input operators of view, the well‐posedness of the open‐loop system is analyzed. Then, under some sufficient conditions expressed by linear matrix inequality, a linear boundary output feedback controller only using boundary measurement is proposed such that the closed‐loop system satisfies GES in absence of external disturbance and satisfies an H∞ performance index when disturbance exists. The well‐posedness of the resulting closed‐loop system is also given via semi‐group theory. Finally, we give numerical examples to verify the performance of the designed boundary controller.