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Finite time analysis of the continuous system is investigated through bothstability and stabilization based on Sum of squares programming. A systematicapproach is proposed to construct Lyapunov function and Control Lyapunovfunction for this objective. The Region of reaching, the set which has theproperty that all trajectories starting from initial point inside it reach tothe origin in finite time, is introduced, and The largest subset of region ofreaching is estimated using Lyapunov based technique. The main results arepresented to give sufficient conditions which can be translated bysemi-definite program. These conditions are provided a feasibility probleminvolving sum of squares constraints. The results of the paper are thenverified by several simulation and numerical examples. Furthermore, oneimportant practical application namely as a super twisting second order slidingmode control also is presented using the proposed result to illustrate itseffectiveness.

Finite time analysis based on Sum of Squares Technique: Applied to the super-twisting second order sliding mode control