Exact Controllability And Exponential Stability Of A Class Of The Conservative Systems

In this paper, we study the exact controllability and exponential stability of the following conservative systems: By introducing special Hilbert space, selecting properly unbounded linear operators A0,C0 and input function u, out function y, firstly, we can formulate the equations (1) as the following two order infinite dimensional linear systems: In order to deal with the exact controllability and exponential stability of systems (1), this paper study the property of A0,C0, and formulate the systems (2) as Weiss Regular linear systems∑(A, B, C, D): Where A is the generator of strongly continuous semigroup on the Hilbert space X, input operator B and output operator C are unbounded linear operators. And in this paper we prove (3) is a conservative system. Furthermore the exact controllability and exponential stability of the equations (1) is proved.