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The convex approach to the absolute stability problem is considered. Gapski and Geromel's algorithm for computing Zames-Falb multipliers, used in determining stability, treats the problem as an optimization problem. It is found that their algorithm may terminate prematurely in some cases, failing to find the optimal multiplier. We propose an improvement that always finds an ascent direction and a multiplier that improves the objective function whenever one exists.

A MIMO negative feedback interconnection of a discrete-time LTI system and a repeated time-invariant, monotone nonlinearity are considered. Kulkarni and Safonov (2001) derived the largest class of multipliers that can be used to show stability of such feedback systems. This paper demonstrates in a simple way that these multipliers can be computed efficiently from the solution of a linear matrix inequality (LMI). It is also shown how the structure of the problem can be exploited to reduce its complexity.

Summary Five very severe post-transfusion reactions occurring in a hospital within a one month period are reported. The reactions were characterized by profuse generalized bleeding, cyanosis and severe hypotension. Marked thrombolysis was the only abnormality observed in the single adequately studied case to account for the bleeding. Four of the 5 patients died, 3 of them within 3 hours and the fourth after 3 days. Bacteriologic investigations of the blood flasks stored at the time showed that 15 out of 32 were contaminated, six of them by Gram negative bacilli. Four of these microorganisms appeared to be very similar and one of them was identified as Aerobacter liquefaciens. Their pathogenicity was confirmed in rabbits and dogs. Contamination was due to faulty sterilization of the equipment used for blood re-collection. Resume Dans l'espace d'un mois, 5 reactions post-transfusionnelles tres graves ont ete observees dans un hopital. Les reactions etaient caracterisees par des hemorragies generalisees et diffuses, de la cyanose et une hypotension grave. Dans le seul cas qui a pu etre etudie en detail la thrombolyse etait la seule cause qui puisse expliquer les hemorragies. 4 des 5 patients sont morts, 3 d'entre eux dans les 3 heures et le quatrieme 3 jours apres les transfusions. Les examens bacteriologiques pratiques sur les conserves de sang preparees a cette periode ont montre que 15 flacons sur 32 etaient contamines, dont six par des bacilles gram negatif. Parmi ces micro-organismes, 4 semblaient etre de meme souche et l'une d'entre elles a pu etre identifiee comme etant constituee par Aerobacter liquefaciens. La pathogenicite de ces micro-organismes a ete confirmee par des examens pratiques sur des lapins et des chiens. La contamination etait due a une sterilisation defectueuse du materiel de prises de sang. Zusammenfassung Es wird uber 5 sehr schwere Transfusionszwischenfalle berichtet, die im selben Spital innert eines Monats beobachtet wurden. Die Empfanger zeigten generalisierte Blutungen, waren zyanotisch und wiesen eine schwere Hypotension auf. Im einzigen eingehender unter-suchten Fall beruhten die Blutungen auf einer ausgesprochenen Thrombolyse. 4 der 5 Patienten starben, 3 innert 3 Stunden, einer nach 3 Tagen. Die bakteriologische Untersuchung der Blutkonservenreste ergab in 15 von 32 Fallen einen positiven Befund. Von 6 Konserven wurden gramnegative Keime gezuchtet. 4 dieser Keime waren sehr ahnlich; einer wurde als Aerobacter liquefaciens identifiziert. Die bakteriellen Verunreinigungen beruhten auf einer fehlerhaften Sterilisation der Transfusionsgerate.