Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing

A method of a Lyapunov functions design based on resolving of the first-order partial differential equation of a special type is presented. A successful resolution of this equation guaranties a finite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. It is also provides an analytical formula for an upper bound of the corresponding reaching time. The suggested method is applied to the problem of a stability analysis and a reaching time estimation of the, so-called, ldquosuper-twistingrdquo controller. The estimation accuracy is confirmed by numerical example.