Comments and observations on the passivity of descriptor systems in state space

Sajja, Surya Shravan Kumar; Corless, Martin; Zeheb, E.; Shorten, Robert

doi:10.1080/00207179.2012.720383

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…Consider a system described by (1) that satisfies rank condition (12). There exist matrices K and L, with I − KD non-singular, such that objectives (9) and (10) hold if and only if the zero output dynamics (22) are stable and have a maximum index of two.…”

Section: Zero Output Dynamicsmentioning

confidence: 99%

“…We now give some results that are important for our discussion. Note that some of these have appeared in preliminary form in our previous papers [22,17,16] Hence, the system resulting from (2) applied to (1) is given by…”

Section: Appendixmentioning

confidence: 99%

“…The index of (E, A) or system (22) is the smallest integer k ≥ 0 for which the rank of (A −1 E) k+1 equals the rank of (A −1 E) k .…”

Section: Zero Output Dynamicsmentioning

confidence: 99%

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On the SPRification of Linear Descriptor Systems via Output Feedback

Corless

Zeheb

Shorten

2019

IEEE Trans. Automat. Contr.

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We consider input-output systems in descriptor form and ask when such systems can be rendered SPR (strictly positive real) via output feedback. Time and frequency domain conditions are given to determine when and how this is possible. In addition, a synthesis procedure for controller design is also derived. Together, the results provide a complete answer to when a linear descriptor system can be made SPR via output feedback, and give a recipe for design of the feedback controller when it exists. Simple examples are given to illustrate our results and to demonstrate their efficacy.

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Section: Zero Output Dynamicsmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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On the SPRification of Linear Descriptor Systems via Output Feedback

Corless

Zeheb

Shorten

2019

IEEE Trans. Automat. Contr.

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“…This work builds on our previous works on the topic. Order reduction ideas based on full rank decompositions were first introduced in [15] and [16]. These results were developed further in [12] and [13].…”

Section: Introductionmentioning

confidence: 99%

A Note on Order and Index Reduction for Descriptor Systems

Corless¹,

Shorten²

2021

Preprint

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We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results.

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