A finite-time convergent algorithm for systems of relative degree more than one

This paper presents a data-driven homogeneous continuous super-twisting algorithm for systems of relative degree more than one, which is globally convergent to the origin for a finite time for any initial condition and also robust with respect to disturbances with a bounded changing rate. The designed technique generalizes the seminal continuous super-twisting algorithm, which was proven to be highly effective for stabilization of both system state and its derivative, to systems of relative degree more than one. This advance leads to a possibility of applying a continuous finite-time stabilization control law to technical plants, where a conventional sliding mode control cannot be reliably employed due to effects pertinent to its discontinuous nature, such as short circuiting. Typical examples of industrial electronics devices where the designed technique could be used include induction motors, anti-lock braking systems, vibration attenuators, and many others. This paper presents a homogeneous continuous super-twisting algorithm for systems with relative degree more than one.