  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.
