Abstract
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is hard to apply to the considered problems. The unstable dynamics of the heat equation are treated by combining the finite-dimensional spectral truncation method and the dynamics compensation method. By introducing additional finite-dimensional actuator/sensor dynamics, the unbounded stabilization/observation turns to be a bounded one. As a result, the controller/observer design becomes more easier. Both the full state feedback stabilizer and the state observer are designed. The exponential stability of the closed-loop and the wellposedness of the observer are obtained.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.