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Algebraic characterizations for positive realness of descriptor systems. (English) Zbl 1157.93011

Summary: Algebraic characterizations for the positive realness of descriptor systems are studied. It is shown that the positive realness of descriptor systems can be determined by solving a linear matrix inequality, and hence the celebrated positive real lemma for standard state space systems is extended to descriptor systems. In addition, the lossless positive realness of both standard state space systems and descriptor systems is characterized explicitly based on the controllable staircase forms of standard state space systems and the generalized controllable staircase forms of descriptor systems, respectively.

MSC:

93B25 Algebraic methods
93B40 Computational methods in systems theory (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
65F35 Numerical computation of matrix norms, conditioning, scaling
15A22 Matrix pencils
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