In this paper,the practical stability and the estimates of practical stability domains of a kind of dynamical system are discussed by employing a Lyapunov method,some sufficient conditions of the existense of the motions invariant set and estimates of practical stability domains of a kind of dynamical system are obtained,which improve the result in the proceeding literature.

Firstly, we ll study the boundary control problem of heat equation with a destabilizing term, and the exponential stability estimate under the given boundary condition.