On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Anders Rantzer

doi:10.1109/TAC.2015.2465571

On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift

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An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries. This is useful in the context large-scale optimization.

Originalspråk	engelska
Sidor (från-till)	1346-1349
Tidskrift	IEEE Transactions on Automatic Control
Volym	61
Nummer	5
DOI	https://doi.org/10.1109/TAC.2015.2465571
Status	Published - 2016

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10.1109/TAC.2015.2465571

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Holmqvist, A., Andersson, N., Cervin, A., Mannesson, A., Gattami, A., Ghulchak, A., Papadopoulos, A. V., Rantzer, A., Robertsson, A., Sootla, A., THEORIN, A., Bernhardsson, B., Olofsson, B., Wittenmark, B., Grussler, C., Johnsson, C., Madjidian, D., Johannesson, E., Magnusson, F., Ståhl, F., Como, G., Chasparis, G., Turesson, G., Dressler, I., Åkesson, J., Cho, J. H., Årzén, K., Åström, K. J., Sou, K. C., Mårtensson, K., Berntorp, K., Soltesz, K., Lessard, L., Hast, M., Rönn, M., Ansbjerg Kjær, M., Maggio, M., Kristalny, M., Garpinger, O., From, P. J., Larsson, P., Giselsson, P., Johansson, R., Hägglund, T., Vladimerou, V., Romero Segovia, V., Aurelius, A., Cedersjö, G., Bür, K., Dellkrantz, M., Du, M., Amani, P., Larsson, R., Tärneberg, W., Li, Z., Yin, L., Tufvesson, F., Höst, S., Nilsson, B., Stenström, S., Andersson, J. A., Diehl, S., Dürango, J., Ghazaei Ardakani, M., Forsberg, P., Bengtsson, F., Jörntell, H., Arévalo, C., Führer, C., Andersson, C., Mohammadi, F., Ödling, P., Andersson, M., Kihl, M. & Tunestål, P.
2008/07/01 → 2018/06/30
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title = "On the Kalman-Yakubovich-Popov Lemma for Positive Systems",

abstract = "An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries. This is useful in the context large-scale optimization.",

author = "Anders Rantzer",

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AB - An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries. This is useful in the context large-scale optimization.

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On the Kalman-Yakubovich-Popov Lemma for Positive Systems

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