Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L, C) on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.

Feedback on the Rate and Depth of Chest Compressions during Cardiopulmonary Resuscitation Using Only Accelerometers

Background Quality of cardiopulmonary resuscitation (CPR) is key to increase survival from cardiac arrest. Providing chest compressions with adequate rate and depth is difficult even for well-trained rescuers. The use of real-time feedback devices is intended to contribute to enhance chest compression quality. These devices are typically based on the double integration of the acceleration to obtain the chest displacement during compressions. The integration process is inherently unstable and leads to important errors unless boundary conditions are applied for each compression cycle. Commercial solutions use additional reference signals to establish these conditions, requiring additional sensors. Our aim was to study the accuracy of three methods based solely on the acceleration signal to provide feedback on the compression rate and depth. Materials and Methods We simulated a CPR scenario with several volunteers grouped in couples providing chest compressions on a resuscitation manikin. Different target rates (80, 100, 120, and 140 compressions per minute) and a target depth of at least 50 mm were indicated. The manikin was equipped with a displacement sensor. The accelerometer was placed between the rescuer's hands and the manikin's chest. We designed three alternatives to direct integration based on different principles (linear filtering, analysis of velocity, and spectral analysis of acceleration). We evaluated their accuracy by comparing the estimated depth and rate with the values obtained from the reference displacement sensor. Results The median (IQR) percent error was 5.9% (2.8-10.3), 6.3% (2.9-11.3), and 2.5% (1.2-4.4) for depth and 1.7% (0.0-2.3), 0.0% (0.0-2.0), and 0.9% (0.4-1.6) for rate, respectively. Depth accuracy depended on the target rate (p < 0.001) and on the rescuer couple (p < 0.001) within each method. Conclusions Accurate feedback on chest compression depth and rate during CPR is possible using exclusively the chest acceleration signal. The algorithm based on spectral analysis showed the best performance. Despite these encouraging results, further research should be conducted to asses the performance of these algorithms with clinical data.