Sliding Mode Control Design: a Sum of Squares Approach
  This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop dynamics. The method is proposed to design a control that guarantees both asymptotic and finite time stability given helped by (bilinear) sum of squares programming. The approach introduces an iterative algorithm to search over sliding mode manifold and Lyapunov function simultaneity. In the case of local stability it concludes also the subset of estimated region of attraction for reduced order sliding mode dynamics. The sliding mode manifold and the corresponding Lyapunov function are obtained if the iterative SOS optimization program has a solution. Results are demonstrated employing the method for several examples to show potential of the proposed technique. 
Sina Sanjari, Sadjaad Ozgoli
cs.SY