  In this paper, the stability and stabilization problem of positive nonlinear
systems, described by the Takagi-Sugeno discrete-time fuzzy model, is studied.
The proposed approach is based on the linear co-positive Lyapunov function and
parallel distributed controller. Necessary and sufficient conditions for the
existence of a state feedback controller, which guarantees the positivity and
stability of the closed-loop system, are obtained by a new approach as linear
programming, and to solve it and obtain the controller coefficients, the
optimal Convex Optimization algorithm is used. Moreover, the design of the
robust controller has been considered. Finally, a numerical and practical
example is presented to illustrate the validity and effectiveness of the
designed method. Keywords: Linear Programming, Co-positive Linear Lyapunov
function, Takagi-Sugeno Fuzzy Systems, Positive Systems.
