A polytopic strategy for improved non-asymptotic robust control via implicit Lyapunov functions

This paper is concerned with finite- and fixed-time robust stabilization of uncertain multi-input nonlinear systems via the implicit Lyapunov function method. Instead splitting system into a linear nominal model an additive perturbation which gathers nonlinearities, parametric uncertainties, exogenous disturbances, methodology hereby proposed preserves some terms in exact polytopic representation leads to design conditions form matrix inequalities. As result, feasible solutions are found where former approaches fail; these have more accurate settling-time estimates reduced control effort. The corresponding law includes well-known high-order sliding modes as particular case. Numerical simulations provided illustrate advantages proposal.