In this article, phase and gain stability margins are defined and studied for a class of nonlinear systems namely, the Lur'e type. The computation algorithms for practical phase and gain margin identification in such systems based on the describing function—harmonic balance technique, circle criterion, and Lyapunov methods involving linear matrix inequalities are presented. The efficacy of the proposed methodologies is validated on a case study.

Background Dumping syndrome is not infrequent after laparoscopic Roux-en-Y gastric bypass (LRYGB) and could result in dreaded complications, such as neuroglycopenia. For those refractory to diet modification or/and medication, regarded as intractable dumping syndrome, revision procedures should be taken into consideration. Herein, we make a video presentation of laparoscopic revision surgery for intractable dumping syndrome with unsatisfactory weight loss. Methods Two diabetic, morbidly obese women (initial body mass index 36.6 and 41.4 kg/m 2 ) presented with intractable dumping syndrome 2 and 3 years after initial LRYGB, respectively. In addition, these patients had insufficient weight loss (body mass index 29 and 31 kg/m 2 ). Laparoscopic revision procedure of loop duodenojejunal bypass with sleeve gastrectomy was conducted to relieve their intractable conditions. Results The mean operation time was 174 min (160 and 188), and the average blood loss was 60 mL (50 and 70). There was no intraoperative complication. Both patients had uneventful postoperative courses, and the average postoperative hospital stay was 2 days. The uncomfortable symptoms relieved successfully after the revision surgery. The Sigstad's score decreased to 2 points 6 months later, and the body mass index reduced to 26 and 28 kg/m 2 .Conclusions Though long-term follow-up is warranted to draw a definite conclusion, loop duodenojejunal bypass with sleeve gastrectomy for pyloric restoration and malabsorptive effect remains an acceptable revision procedure to relive intractable dumping syndrome and successfully maintain sustained weight loss in our patients.

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