The paper deals with the problem of finite-time stability analysis of relay control systems described by ordinary differential equations and functional differential equations with discontinuous right-hand sides. It presents some extensions of Lyapunov theorems to this class of systems and discusses a method of an analytical construction of Lyapunov functions, which helps to design the unified Lyapunov function candidate for whole class of relay second-order sliding mode control systems. The theoretical results are supported by numerical simulations for systems with ‘twisting’, ‘nested’ and ‘suboptimal’ controllers.