Abstract: The numerical method to solve the problem of static output feedback(SOF) H_∞ control problem for the linear time-invariant system is addressed under the framework of sequential linear programming matrix method(SLPMM) based on target function linearization.An improved SLPMM is proposed,which reduces the calculation iterations of initial feasible solution and gives an initial estimation of H_∞ norm through solving an LMI(linear matrix inequality) eigenvalue problem,is proposed in the paper.Finally an example of designing a longitudinal controller for an aircraft is given to demonstrate the validity of the algorithm.