  This paper proposes a line integral Lyapunov function approach to stability
analysis and stabilization for It\^o stochastic T-S models. Unlike the
deterministic case, stability analysis of this model needs the information of
Hessian matrix of the line integral Lyapunov function which is related to
partial derivatives of the basis functions. By introducing a new method to
handle these partial derivatives and using the property of state-dependent
matrix with rank one, the stability conditions of the underlying system can be
established via a line integral Lyapunov function. These conditions obtained
are more general than the ones which are based on quadratic Lyapunov functions.
Based on the stability conditions, a controller is developed by cone
complementarity linerization algorithm. A non-quadratic Lyapunov function
approach is thus proposed for the stabilization problem of the It\^o stochastic
T-S models. It has been shown that the problem can be solved by optimizing sum
of traces for a group of products of matrix variables with linear constraints.
Numerical examples are given to illustrate the effectiveness of the proposed
control scheme.
