In this paper new necessary and sufficient conditions for static output feedback robust controller design for linear discrete time-invariant systems has been used. The output feedback robust controller design may be reduced to the problem of finding a feasible point under Biaffine Matrix Inequality constraint. In this paper the BMI problem of the output feedback robust controller design has been reduced to LMIs problem. The proposed LMI based algorithms are computationally simple and tightly connected with the Lyapunov function, quadratic stability, guaranteed cost and LQ optimal state feedback design. The structure of the output gain matrix can be prescribed by the designer.