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L_\infty -instability of large-scale interconnected systems using orthogonal decomposition and exponential weighting

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In this paper, we give an explicit characterization of the orthogonal complement of the "set of stabilizing inputs" for an unstable convolution operator. This characterization involves the right-coprimne factorization of the transfer function matrix of the convolution operator. Using this characterization, we then explicitly demonstrate specific inputs that would causeL_2-instability in a given large-scale interconnected system, using the technique of orthogonal decomposition of the input space. Finally, using the technique of exponential weighting, we give a general result that can be used to establish theL_{infty}-instability of a given system by proving that an associated system isL_2-unstable. In this way, one can obtainL_{infty}-instability criteria corresponding to virtually every known criterion forL_2-instability that uses the technique of orthogonal decomposition.

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Circuits and Systems, IEEE Transactions on  (Volume:27 ,  Issue: 10 )