Control of Impulsive Systems Via High-Order Fully Actuated System Approach

This article studies the problem of designing the controller for the stabilization of nonlinear control systems with impulsive effects via high-order fully actuated (HOFA) system approach. A matrix norm inequality that connects the matrix norm to the eigenvalues of the matrix is obtained, providing the theoretical basis for the utilization of the HOFA system approach in controlling high-order nonlinear impulsive systems. The analysis on the closed-loop systems derives the stability criteria of nonlinear control systems with impulsive effects via the HOFA system approach. This work not only extends the application of the HOFA system approach to nonlinear impulsive systems for the first time but also introduces a new nonlinear control technique for the control of impulsive systems. With the proposed approach to design the controller, two examples demonstrate the design procedure and show the effectiveness of the theoretical results.