Stabilization of non-autonomous infinite-dimensional systems depending on a parameter

ABSTRACT

In this paper, we investigate the practical stabilization of non-autonomous infinite-dimensional systems depending on a parameter. By the Lyapunov method, several sufficient conditions are provided to obtain the practical stabilization of two classes of non-autonomous semilinear evolution equations in Hilbert spaces. We propose some classes of memoryless state linear and nonlinear feedback controllers. Numerical examples are given to illustrate the validity of the proposed theoretical results.

KEYWORDS:

• Non-autonomous infinite-dimensional system
• practical stabilization
• partial differential equation
• feedback controller
• Lyapunov method

Acknowledgments

The authors would like to express their deep gratitude to the anonymous reviewers for their valuable comments and suggestions, which led to an improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Data sharing not applicable to this article as no data sets were generated or analysed during the current study.