A new approach to robust control design is considered. It is based on Implicit Lyapunov Function method. An algorithm of robust finite-time stabilization for a quasi- linear multi-input disturbed system is developed. A new high- order sliding mode control algorithm is deduced. Procedures for tuning of control parameters are presented. They are based on Linear Matrix Inequalities (LMI). Aspects of practical implementation of developed algorithms are discussed. A scheme for chattering reduction is proposed. Theoretical results are supported by numerical simulations.