Multivariable gain-phase and sensitivity integral relations anddesign trade-offs
Jie Chen
Automatic Control, IEEE Transactions on
Volume 43, Issue 3, Mar 1998 Page(s):373 - 385
Digital Object Identifier   10.1109/9.661594
Summary:We present several extensions of the classical Bode integral relations to multivariable systems. The main contributions are an extended gain-phase integral formula and an extended sensitivity integral relation. These results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems. In particular, they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single-input/single-output systems. Both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

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