Relationship between robustness μ-analysis and classical stability margins

The classical stability margins, i.e. gain and phase margin, have been adopted for a long time as the criteria for system stability analyses. These margins, originally used for Single-Input-Single-Output (SISO) systems, have been extended for Multi-Input-Multi-Output (MIMO) systems using the μ-analysis. With the present definition for formulating their uncertainty, there is a one-to-one correspondence between μ-value and guaranteed bounds on the stability margins. However, present definitions always appear in a certain fixed ratio between the guaranteed bounds on gain and phase margin for a specified μ-value. Therefore, bounds on only either the gain or phase margin individually can be matched by performing the μ-analysis, thus resulting in conservative control design. In this paper, a new method with which the μ-value can be made to associate with arbitrarily chosen bounds on gain and phase margins, so that a more specific stability analysis can be performed resulting in a less conservative control system design. An example is given to demonstrate this new technique