On a theorem of Redheffer concerning diagonal stability
- Shorten, Robert
- Narendra, Kumpati S.
DOIAbstract
AbstractAn important problem in system theory concerns determining whether or not a given LTI system x˙=Ax is diagonally stable. More precisely, this problem is concerned with determining conditions on a matrix A such that there exists a diagonal matrix D with positive diagonal entries (i.e. a positive diagonal matrix), satisfying ATD+DA=-Q<0. While this problem has attracted much attention over the past half century, two results of note stand out: (i) a result based on Theorems of the Alternative derived by Barker, Berman and Plemmons; and (ii) algebraic conditions derived by Redheffer. This paper is concerned with the second of these conditions. Our principal contribution is to show that Redheffer’s result can be obtained from the Kalman–...
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