  In this paper, a concurrent learning based adaptive observer is developed for
a class of second-order linear time-invariant systems with uncertain system
matrices. The developed technique yields an exponentially convergent state
estimator and an exponentially convergent parameter estimator. As opposed to
persistent excitation required for parameter convergence in traditional
adaptive methods, excitation over a finite time-interval is sufficient for the
developed technique to achieve exponential convergence. Simulation results in
both noise-free and noisy environments are presented to validate the design.
