Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2007-010 (February 09, 2007)
Robust stability analysis of uncertain interconnection in the behavioral framework
by Kiyotsugu Takaba
This paper considers the robust stability of the interconnection of a linear time-invariant differential nominal system and passive uncertainties in the behavioral framework. A generalized version of the well-known passivity theorem is formulated by using quadratic differential forms. Based on the generalized passivity theorem, it is proved that, if the nominal system is ŽÁ-passive, the interconnection is robustly stable against
strictly (-ŽÁ)-passive uncertainty. Moreover, we show that the ŽÁ-passivity of the nominal system is a necessary and sufficient condition for the robust stability with regularity constraint of the uncertain interconnection.