Mild solution and uniform exponential stability of the time varying singular distributed parameter systems in Hilbert space

Mild solution and uniform exponential stability of time varying singular distributed parameter control system are discussed via GE-semigroup and the theory of GE mild evolution operator in Hilbert space. The sufficient conditions concerning the existence and uniqueness of the solution, and the equivalent conditions of uniform exponential stability are obtained. This research is very important for studying the solution and uniform exponential stability of the singular distributed parameter control system.