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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 functions H . Given that the k th subsystem is perturbed from G_{k} = N_{rk}D_{k}^{-1} to \tilde{G}_{k} = (N_{rk} + \Delta N_{rk})(D_{k} + \Delta D_{k})^{-1} and that the system Sois H -stable, we derive a computationally efficient necessary and sufficient condition for the H -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.

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