Robust stability analysis of uncertain interconnection in the behavioral framework
Abstract
This paper considers the robust stability of the interconnection ofa 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 strongly Phi-passive, the interconnection is robustly stable against -Phi -passive uncertainty. Moreover, we show that the strong Phi-passivity of the nominal system is a necessary and sufficient condition for the robust stability of a "regular" interconnection.
