Automated falling detection is one of the important tasks in this ageing society. Such systems are supposed to have little interference on daily life. Doppler sensors have come to the front as useful devices to detect human activity without using any wearable sensors. The conventional Doppler sensor based falling detection mechanism uses the features of only one sensor. This paper presents falling detection using multiple Doppler sensors. The resulting data from sensors are combined or selected to find out the falling event. The combination method, using three sensors, shows 95.5% accuracy of falling detection. Moreover, this method compensates the drawbacks of mono Doppler sensor which encounters problems when detecting movement orthogonal to irradiation directions.

Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay exactly faster than . The system contains a dynamic compensator with another state v in the feedback loop, and consists of two states u and v. This problem entirely differs from the one with static feedback scheme in which the system consists only of a single state u. To show the essential difference, some specific property of the spectral subspaces associated with our control system is studied.