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In this paper, the authors present a linear matrix inequality (LMI) approach to the strictly positive real (SPR) synthesis problem: find an output feedback K K K such that the closed-loop system T(s) T(s) T(s) is SPR. The authors establish that if no such constant output feedback K K K exists, then no dynamic output feedback with a proper transfer matrix exists to make the closed-loop system SPR. The existence of K K K to guarantee the SPR property of the closed-loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters. Index Terms-Adaptive control, H 1 control, linear matrix inequality, output feedback, positive real functions.

To offer individualized dental treatment to certain patients who cannot tolerate dental treatment, sedation or general anesthesia is required. The needs could be either medical, mental, or psychological. The most common indications for sedation or general anesthesia are lack of cooperation, multiple morbidities, and pediatric autism. In adults, cognitive impairment and multiple morbidities are most commonly encountered indications. Because of suboptimal home care, incomplete medical history, poor preoperative management, lack of cooperation, and developmental abnormalities, it is a challenge to prepare anesthesia for patients with special needs. The American Society of Anesthesiology (ASA) has proposed guidelines for office-based anesthesia for ambulatory surgery. In patients with ASA physical status IV and V, sedation or general anesthesia for treatment in the dental office is not recommended. The distinction between sedation levels and general anesthesia is not clear. If intravenous general anesthesia without tracheal intubation is chosen for dental procedures, full cooperation between the dentist, dental assistant, and anesthesiologist is needed. Teamwork between the dentist and healthcare provider is key to achieve safe and successful dental treatment under sedation or general anesthesia in the patient with special needs.