  Our main contribution in this article is the achievement of the turnpike
property in its integral and exponential forms for parameter-dependent systems
with averaged observations in the cost functional. Namely, under suitable
assumptions with respect to the matrices that defined the dynamics and the cost
functional, we prove that the optimal control and state for the evolutionary
problem converge in average to the optimal pair of an associated stationary
problem. Moreover, we characterize the closeness between these two optimal
solutions, proving that over a large time interval, they are exponentially
close.
