Finite time analysis based on Sum of Squares Technique: Applied to the super-twisting second order sliding mode control
For control theorists, this provides a systematic SOS-based method for finite-time analysis, but it is an incremental extension of existing SOS techniques to finite-time stability.
This paper proposes a systematic sum-of-squares (SOS) programming approach to construct Lyapunov and control Lyapunov functions for finite-time stability and stabilization of continuous systems. The method estimates the largest subset of the region of reaching and is applied to super-twisting second-order sliding mode control, with numerical examples verifying the results.
Finite time analysis of the continuous system is investigated through both stability and stabilization based on Sum of squares programming. A systematic approach is proposed to construct Lyapunov function and Control Lyapunov function for this objective. The Region of reaching, the set which has the property that all trajectories starting from initial point inside it reach to the origin in finite time, is introduced, and The largest subset of region of reaching is estimated using Lyapunov based technique. The main results are presented to give sufficient conditions which can be translated by semi-definite program. These conditions are provided a feasibility problem involving sum of squares constraints. The results of the paper are then verified by several simulation and numerical examples. Furthermore, one important practical application namely as a super twisting second order sliding mode control also is presented using the proposed result to illustrate its effectiveness.