Prescribed-Instant Stabilization for Second-Order Systems With Unmatched Uncertainties.

This paper investigates the stabilization of second-order systems subject to mismatched uncertainties. We present prescribed-instant stability, a unique form of prescribed-time stability, where the uncertain second-order system is driven to the origin exactly at the prescribed time instant Tp. A strict Lyapunov method proof is presented on two sides, i.e., the system converges to and reaches zero not after nor before Tp. The former is very common in existing articles about prescribed-time stability. The latter is usually ignored, but it is very important to obtain the prescribed-instant stability in this paper. We present the controllers in two cases based on different mismatched uncertainties. Simulations validate the effectiveness of the proposed method.