  In this paper we present an abstraction algorithm that produces a finite
bisimulation quotient for an autonomous discrete-time linear system. We assume
that the bisimulation quotient is required to preserve the observations over an
arbitrary, finite number of polytopic subsets of the system state space. We
generate the bisimulation quotient with the aid of a sequence of contractive
polytopic sublevel sets obtained via a polyhedral Lyapunov function. The
proposed algorithm guarantees that at iteration $i$, the bisimulation of the
system within the $i$-th sublevel set of the Lyapunov function is completed. We
then show how to use the obtained bisimulation quotient to verify the system
with respect to arbitrary Linear Temporal Logic formulas over the observed
regions.
