EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

摘要

The exponential stability of a multi-state device is discussed in this paper. We present that the C0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.