Design of robust control Lyapunov function for non-linear affine systems with uncertainty

This study proposes a fractional programming formulation and its solution strategy to construct a robust control Lyapunov function for control affine systems of relatively small size in the presence of disturbances and input constraints. The original formulation is recast as a recursive optimisation problem, and a single optimisation variable is heuristically selected at each round to gradually enlarge the region of attraction for a quadratic Lyapunov function. Two case studies with actuator saturation show the efficacy of the proposed approach.