  The formal analysis and design of control systems is one of recent trends in
control theory. In this area, in order to reduce the complexity and scale of
control systems, finite abstractions of control systems are introduced and
explored. In non-disturbance case, the controller of control systems is often
generated from the controller of finite abstractions. Recently, Pola and
Tabuada provide approximate finite abstractions for linear control systems with
disturbance inputs. However, these finite abstractions and original linear
systems do not always share the identical specifications, which obstructs
designing controller (of linear systems) based on their finite abstractions.
This paper tries to bridge such gap between linear systems and their finite
abstractions.
