To solve the problem of limits on variables

the most intuitive way is to build an optimization model of which the objective function is the variables to be solved and the feasible region is the constraints. By solving maximin problems

the upper limits and lower limits on these variables can be achieved. The advantage of the method based on the optimization model is that it can take all the constraints into consideration. Thus

the results are less conservative or even not conservative at all. Firstly

the optimization model to solve the limits of state variables and measurement variables is introduced briefly. However

as the optimization model is a non-convex model

for non-convex models

the global optimal solution cannot be got. To deal with this problem

a conic optimization model which is used to solve the limits of the measurement variables is then established. The numerical example shows that by solving the conic optimization model not only is the credibility of the results ensured

but also the solving efficiency is improved. This work is supported by National Natural Science Foundation of China (No. 51207136).