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Algebraic theory for robust stability of interconnected systems: Necessary and sufficient conditions

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2 Author(s)
Ming-Jeh Chen ; University of California, Berkeley, CA, USA ; Desoer, C.A.

We consider an interconnected system Somade of linear mulrivariable subsystems which are specified by matrix fractions with elements in a ring of stable scalar transfer functionsH. Given that thekth subsystem is perturbed fromG_{k} = N_{rk}D_{k}^{-1}totilde{G}_{k} = (N_{rk} + Delta N_{rk})(D_{k} + Delta D_{k})^{-1}and that the system SoisH-stable, we derive a computationally efficient necessary and sufficient condition for theH-stability, of the perturbed system. These fractional perturbations are more general than the conventional additive and multiplicative perturbations. The result is generalized to handle simultaneous perturbations of two or more subsystems.

Published in:

Automatic Control, IEEE Transactions on  (Volume:29 ,  Issue: 6 )

Date of Publication:

Jun 1984

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