  We consider a remote state estimation problem in the presence of an
eavesdropper over packet dropping links. A smart sensor transmits its local
estimates to a legitimate remote estimator, in the course of which an
eavesdropper can randomly overhear the transmission. This problem has been well
studied for unstable dynamical systems, but seldom for stable systems. In this
paper, we target at stable and marginally stable systems and aim to design an
event-triggered scheduling strategy by minimizing the expected error covariance
at the remote estimator and keeping that at the eavesdropper above a
user-specified lower bound. To this end, we model the evolution of the error
covariance as an infinite recurrent Markov chain and develop a recurrence
relation to describe the stationary distribution of the state at the
eavesdropper. Monotonicity and convergence properties of the expected error
covariance are further investigated and employed to solve the optimization
problem. Numerical examples are provided to validate the theoretical results.
