Abstract: In this paper, the authors propose that H_∞ sub optimization design problem can be solved by solving two algebraic Riccati inequalities. The advantage of using Algebraic Riccati Inequality is that there may be a set of solutions if there is one solution. In other words, we may have the chance to optimize system's multiple performance indexes at the same time. For example, we can design H_∞/H₂ mixed sub optimization controller based on Algebraic Riccati Inequality. More over, an application example is given to illustrate the main results.