Search

This paper studies the Mittag-Leffler stabilization for unstable infinite dimensional systems actuated by boundary controllers described by time fractional reaction diffusion equations. Via the Riesz basis method, the stable and the unstable part of the considered system are separated. The Kalman rank criterion, which is a classical linear algebra condition, guarantees the stabilizability of the unstable subsystem. Based on these, a controller governed by a finite dimensional system (so called the finite dimensional controller hereafter) is designed to achieve the Mittag-Leffler stability of the closed loop. From infinite to finite, this methodology is a substantial improvement for the existing control laws.

Patients undergoing percutaneous transforaminal endoscopic discectomy (PTED) often complain of unbearable intraoperative pain. This study is to observe clinical effectiveness and safety of intradiscal local anesthetic injection for intraoperative pain relief.Total 268 patients who underwent PTED were analyzed. Patients were divided into intradiscal saline injection group (group C) and intradiscal local anesthetic injection group (group L). Intradiscal mixture was consisted of saline or local anesthetic + methylene blue, the amount of injected mixture was 3 mL. Demographic data, visual analog scale (VAS) and Quebec Back Pain Disability Scale (QBPDS) scores, mean arterial pressure (MAP) and heart rate (HR), total dosage of fentanyl, satisfaction rate of anesthesia and complications were collected at different timepoints.Compared with group C (3.94 ± 0.57), there was a significant reduction of VAS in group L (2.83 ± 0.28) during fibrous annular operation phase (T2). Group L had a lower total dosage of fentanyl (71 [63, 78] μg) and a higher anesthesia satisfaction rate (95.3%) than group C (82 [70, 132] μg and 73.6%, respectively) (P 0.001). MAP and HR were lower in group L than in group C at T2 (P 0.001). Baseline characteristics and QBPDS scores showed no meaningful intergroup differences. Four cases of complications were reported in this study.Intradiscal local anesthetic injection significantly alleviated intraoperative back pain and increased the satisfaction rate of anesthesia, without severe complications, indicating that this technique is a feasible method for intraoperative back pain relief for patients undergoing PTED.