AN ADDITIONAL COMPARISON
As remarked in chapter 5, the mixed ц upper bounds of subsections
2.3 and 2.4 are equivalent. This can be checked on the example of Figure 6.9, which corresponds to the robust stability problem (P4). The 4 plots represent the complex /x upper bound, the mixed / upper bound of subsection 2.4 and the mixed ц upper bound of subsection 2.3 (computed using the /x Analysis and Synthesis Toolbox and the LMI Control Toolbox). As expected, the results obtained with the 3 mixed /x upper bounds are essentially equivalent. The result provided by the LMI Control Toolbox is globally more accurate than the one provided by the /x Analysis and Synthesis Toolbox. Nevertheless, it should be noted that the algorithm of the X Analysis and Synthesis Toolbox is designed in order to minimize the computational burden for large dimension problems. It is moreover possible to use various options, so as to achieve a balance between the accuracy of the result (i. e. the degree of optimality of the result) and the computational requirement.