Abstract
In this paper, connective stability is considered for large scale systems consisting of a number of subsystems and uncertain interconnections. A necessary and sufficient condition of connective stability is derived in terms of linear matrix inequalities (LMIs), under which the overall systems are robustly stable against the uncertainties of the interconnections. This condition gives a useful sufficient condition which lead to an LMI condition even for connective stabilization via decentralized state feedback if an unstructured matrix variable in the LMIs is restricted to a block diagonal one. In this paper, a characterization of this sufficient condition is also derived in frequency domain. It is shown that the condition is equivalent to a familiar ℳ matrix condition which utilizes ℋ∞ norm of each subsystem.
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