Robust H∞ finite-time stability control of a class of nonlinear systems

• Robust H∞ finite-time stability theorems of nonlinear systems are proposed.
• A robust H∞ finite-time stability controller of robotic manipulators is designed.
• Without solving the Hamilton–Jacobi equation and the Riccati equation.
• The closed-loop system is global finite-time stable.
• The closed-loop system has L2-gain less than or equal to γ.

In this paper, a robust H∞ finite-time stability control approach is proposed for a class of nonlinear systems without solving the Hamilton–Jacobi equation and the Riccati equation. First, the concept of robust H∞ finite-time stability is proposed and the corresponding theorem is presented. Then, for a class of common dynamic systems such as robotic manipulators, a robust H∞ finite-time stability controller is designed based on the backstepping method, with which the closed-loop system is not only global finite-time stable but also has L2-gain less than or equal to γ. Finally, some simulations are performed on a robotic manipulator with two degrees of freedom. The results indicate that the proposed control approach is of high effectiveness.