Finite-Time Stability of a Second-Order Bang–Bang Sliding Control Type

Abstract

This paper presents the double chain–integrator finite-time convergence in a closed loop with a second-order bang–bang sliding control. The direct Lyapunov method carried out the stability analysis and the reaching time estimation using a suitable non-smooth strong Lyapunov function. That is, the proposed energy function is strictly positive definite, with a strictly definite negative time derivative. Additionally, the proposed function estimates the reaching time in the presence of matching bounded perturbations. Numerical comparisons with well-known approaches were performed to assess the proposed strategy’s effectiveness.

Keywords

• finite-time stability
• strong Lyapunov function
• sliding mode control