Prescribed-Time Impulsive Control of High-Order Integrator Systems

This article presents a new design of prescribed-time impulsive controllers for the prescribed-time stability (PTS) of high-order integrator systems with a single control input. To deal with the singularity of the control input matrix, a stability result is established based on the algebraic Riccati equation, which derives the explicit parametric control gains of impulsive control. Then, the prescribed-time impulsive control with such parametric control gains is designed to ascertain the convergence of the state transition matrix to a nilpotent matrix and achieve the PTS of high-order integrator systems by adjusting the parameters of control gains at impulsive instants. Aprescribed-time impulsive observer is also proposed for the PTS of the system with an accessible sampled single output. Finally, the validity of the theoretical results is verified by the trajectory tracking of the omnidirectional mobile robots via velocity regulation.