An Asymptotically Convergent Variable Structure Observer Formulation for a Class of Nonlinear Engineering Systems

This work introduces a variable structure velocity observer formulation for a broad class of second order nonlinear engineering systems. The proposed observer formulation incorporates a novel error signal that performs similarly to a sliding-mode observer for larger values of the position observation error and acts as a high-gain term when the position observation error is small. The stability of the observer formulation is validated through a novel Lyapunov-like argument, ensuring the practical asymptotic convergence of the observation error. Specifically, the velocity observation error is guaranteed to converge to a small region near the origin, that can be adjusted to be arbitrarily small by the observation gains. The effectiveness of the observer formulation is examined through numerical simulations on the New England 39-bus power system, a testing platform comprising 39 buses and 10 generators.