For a linear system with structured uncertainties, the conditions of controllability and observability depend on interval parameters. In this paper, we will analyze this problem using the monotonicity conditions with respect to interval parameters. But, in some cases, the monotonicity conditions do not hold on the whole parameter region. Then, we will present controllability and observability analysis using monotonization methods. It can be applied to the cases where the monotonicity conditions do not hold. An example illustrating our method is given.