The Lyapunov Function Design for the Stability Analysis of the “Italian Version” of the Second Order Sliding Mode Controllers

The paper deals with the problem of a finite-time stability analysis of relay and switching systems described by discontinuous functional-differential equations of a special class. One method of the Lyapunov function designing is presented and demonstrated for the “Italian version” of the second order sliding mode controller, which is also known as “sup-optimal controller”. The theoretical results are supported by numerical simulations.