AUTHOR KEYWORDS: Lyapunov function; Measure theory; Sliding mode control; Sliding surface design; SMC; Time optimal control INDEX KEYWORDS: Discrete time control systems; Lyapunov functions; Optimal control systems; Problem solving; Trajectories, Lyapunov functionals; Measure theory; Nonlinear control problems; Sliding surface; SMC; System trajectory; Time optimal control; Time-optimal control problems, Sliding mode control PUBLISHER: Inderscience Enterprises Ltd.