Online Output-Feedback Parameter and State Estimation for Second Order Linear Systems

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.