Stability analysis of 2-sliding mode algorithms via convex optimisation

This paper pursues the construction of a valid strong Lyapunov function for second-order sliding mode algorithms, usually employed for control, observation, and differentiation purposes. The developed solution is based on combining convex representations of such algorithms with the direct Lyapunov method, which leads to stability conditions expressed in the form of linear matrix inequalities. The proposed methodology enlarges the set of gains for which the algorithms are guaranteed stable in prior literature.