Stability margins in traditional and Second Order Sliding Mode Control

Sliding Mode Control (SMC) and Second Order Sliding Mode (2-SMC) are robust techniques that are used in many applications including aerospace control. In order to be certified for practical applications, a control design must demonstrate not only stability in the ideal case, but stability when subjected to dynamic perturbation i.e. stability margins. In Linear Time Invariant (LTI) systems the mostly accepted stability measures are phase margin and gain margin. However, these margins cannot be strictly computed for nonlinear systems; in particular, they cannot be computed for SMC and 2-SMC controllers, and this has delayed acceptance of such techniques in practical applications. This paper is intended to open a discussion of how stability margins compatible with tradition and with modern nonlinear methods might be defined in SMC and 2-SMC systems.