  We consider the problem of studying the performance of greedy algorithm on
sensor selection problem for stable linear systems with Kalman Filter.
Specifically, the objective is to find the system parameters that affects the
performance of greedy algorithms and conditions where greedy algorithm always
produces optimal solutions. In this paper, we developed an upper bound for
performance ratio of greedy algorithm, which is based on the work of Dr.Zhang
\cite{Sundaram} and offers valuable insight into the system parameters that
affects the performance of greedy algorithm. We also proposes a set of
conditions where greedy algorithm will always produce the optimal solution. We
then show in simulations how the system parameters mentioned by the performance
ratio bound derived in this work affects the performance of greedy algorithm.
