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

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.