Stabilization With Prescribed Instant via Lyapunov Method

This letter presents a prescribed-instant stabilization approach to high-order integrator systems by the Lyapunov method. Under the presented controller, the settling time of controlled systems is independent of the initial conditions and equals the prescribed time instant. With this method, the prescribed-instant stabilization method can be easily proved and extended. To be more specific, two differential inequalities of Lyapunov functions are presented to clamp/constrain the settling time to the prescribed time instant from both the left and right sides. This thought serves as an example to present a general framework to verify the designed stabilization property. Actually, the prescribed-time stability (PSTS) [1] can not prescribe the exact settling time. It can only prescribe the upper bound of the settling time and is different with this work. The detailed argumentation will be presented after a brief review of the existing important research.