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Generalized eigenvalue passivity assessment of descriptor systems with applications to symmetric and singular systems


Luc Knockaert, Department of INTEC–IBCN, St. Pietersnieuwstraat 41, B-9000, Ghent, Belgium.



This paper proposes general eigenvalue-based passivity tests for descriptor state space systems, extending the already available tests for standard state space systems. Generalized eigenvalue tests are proposed to identify passivity violations in the positive-real and bounded-real cases. The important practical case of singular descriptor state space systems is also treated. The proposed passivity tests for descriptor systems can be used in the important case of symmetric (reciprocal) systems, as symmetric systems can always be cast in an explicitly reciprocal descriptor state space format. Also, passivity violation assessment methods are developed in the important case of strictly proper symmetric systems, as in that case the classical test matrices for passivity assessment are undefined. Finally, some pertinent numerical examples are given to demonstrate the usefulness and scope of the different passivity violation assessment tests. Copyright © 2012 John Wiley & Sons, Ltd.