Wireless endoscopic capsules can transmit the picture of the inside of the digestive tract to the external receiver for the purpose of gastrointestinal diseases diagnose. The localization of the capsule is needed to correlate the picture of detected anomalies with the particular fragment of intestine. For this purpose, the analysis of wireless transmission parameters can be applied. Such methods are affected by the impact of the human body on the electromagnetic wave propagation that is specific to the anatomy of individual person. The article presents the algorithm of localization of endoscopic capsules with wireless transmitter based on the detection of phase difference of received signals. The proposed algorithm uses simplified human body models that can change their dielectric properties in each iteration to improve the location of the capsule endoscope. Such approach allows to reduce localization error by around 12 mm (15%) and can by used for patients of different physique without the need of the numerical models of individual body.

AbstractThe Caputo-Fabrizio definition of the fractional derivative is applied to minimum energy control of fractional positive continuous- time linear systems with bounded inputs. Conditions for the reachability of standard and positive fractional linear continuous-time systems are established. The minimum energy control problem for the fractional positive linear systems with bounded inputs is formulated and solved.

The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f(e) of the nonlinear parts satisfy the condition
k₁e  ≤ f(e) ≤ k₂e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (–¹/k₁,  –¹/k₂).