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Robust stability under additive perturbations

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2 Author(s)
Bhaya, A. ; University of California, Berkeley, CA, USA ; Desoer, C.A.

We consider a MIMO linear time-invariant feedback system1 S(P, C) which is assumed to be u -stable. The plant P is subjected to an additive perturbation \Delta P which is proper but not necessarily stable. We prove that the perturbed system is u -stable if and only if \Delta P[I + Q.\Delta P]^{-1} is u -stable. (Here Q: = C(I + PC)^{-1}.)

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Automatic Control, IEEE Transactions on  (Volume:30 ,  Issue: 12 )