Abstract: We studied the stability of a class of hyperbolic systems with balance laws under delayed feedback control and the spectral analysis of the system operator  by using the strictly weighted Lyapunov function method and asymptotic analysis technique. Firstly, the well-posedness of the systems was verified by using operator semigroup theory. Secondly, the exponential stability of the closed-loop system was analyzed by constructing a strictly weighted Lyapunov function. Finally, according to  the asymptotic analysis technique, the asymptotic expressions of eigenvalues and eigenfunctions were obtained. The result shows that the system is exponentially stable when the feedback parameters and delayed value satisfy certain inequality constraints, and when the modulus of eigenvalues tends to positive infinity, the real part of the eigenvalues tends to a negative constant.

Key words: hyperbolic systems with balance laws, delayed feedback, spectral analysis, exponential stability