Correction to: ‘Strict positive realness of descriptor systems in state space’, by Ezra Zeheb, Robert Shorten & S. Shravan K. Sajja (2010), International Journal of Control, 83 (9), pp. 1799–1809.
The authors would like to correct the following errors that were missed at proof stage:
The results in the paper apply only to stable index-1 descriptor systems. Note also that after Remark 5 up to Section 5 we refer to KYP-SPR throughout.
In Part (C) of Theorem 3 on page 1805:
The proof of Part (C) follows directly from [14] (Th. 2.1) with d not zero, by writing the conditions for KYP-SPR of H(jω) in terms of conditions on .
In Part (D) on page 1805:
Using Parts (A) and (B), SPR of H(jω) is equivalent to SPR of the transfer function in (49b).
Should read:
Using Parts (A) and (B), KYP-SPR of H(jω) of (2) can be checked with a spectral condition derived from (49b).
On page 1806, in Remark 7 the text:
det[sE–A] should read det[sI–EA −1] and
should read
det[sI–EM
−1]. Also note that d ≠ 0.
On page 1807 the text:
It follows from Part (C) of the proof of Theorem 3, that the descriptor system is stable if there exists a CQLF for the following dynamic systems:
Should read:
It follows from Part (C) and Part (D) of the proof of Theorem 3, that the descriptor system is KYP-SPR if there exists a CQLF for the following dynamic systems:
In Remark 9 on page 1807:
switched descriptor system is stable
Should read:
switched descriptor system is stable since the consistency spaces and the kernel of E intersect only at the origin”Footnote1.
An endnote is also added:
Notes
1. A full argument and proof is given in “On dimensionality reduction and stability of a class of switched descriptor systems” Sajja; Corless; Zeheb; Shorten. This paper was formerly titled as “Stability conditions for a class of switching descriptor systems”, Provisonally accepted, Automatica, 2011.