Observability of Nonlinear Systems

We consider the observability of systems of the form = Ax +Nx, y = Fx, where A is a linear operator and N and F are nonlinear.We show that if the system is linearized about an equilibriumpoint x_e and the linearized system is continuously initiallyobservable, then the nonlinear system is continuously initiallyobservable in some neighbourhood of x_e. We then look at conditionsunder which solutions of the nonlinear system can be extendedfor all time and consider the problem of stabilizing the systemby feedback controls such that the solutions are eventuallyin the observability neighbourhood of x_e. Finally, we applythese ideas to two systems: a wave equation and a diffusionequation with nonlinear perturbations and nonlinear observations.     

GUIDELINES FOR WHOLE-BODY VIBRATION HEALTH SURVEILLANCE

There is strong epidemiological evidence that occupational exposure to WBV is associated with an increased risk of low back pain (LBP), sciatic pain, and degenerative changes in the spinal system, including lumbar intervertebral disc disorders. A prototype health surveillance scheme for WBV is presented in this paper. Surveillance is the collection, analysis, and dissemination of data for the purpose of prevention. The aims are to assess health status and diagnose vibration-induced disorders at an early stage, to inform the workers on the potential risk associated with vibration exposure, to give preventive advice to employers and employees and to control whether preventive measures which have been taken, were successful. It is suggested that a pre-placement health examination should be offered to each worker who will be exposed to WBV so as to make the worker aware of the hazards, to obtain baseline health data, and to identify medical conditions that may increase the risk due to WBV. The case history should focus on personal history, work history, and leisure activities involving driving of vehicles. The personal medical history should detail back pain complaints, disorders in the spine, any injuries or surgery to the musculoskeletal system. A physical examination on the lower back should be performed on workers who have experienced LBP symptoms over the past 12 months. The preplacement examination should be followed by periodic health reassessment with a regular interval according to the legislation of the country. It is suggested that periodic medical examination should be made available at least every 2 years to all workers who are exposed to WBV. Any change in vibration exposure at the workplace should be reported by the employer. If an increase in vibration exposure or a change in health status have occurred, the medical re-examination should be offered at shorter intervals at the discretion of the attending physician. There should be a periodic medical examination, which includes recording any change in exposure to WBV. The findings for the individual should be compared with previous examinations. Group data should also be compiled periodically. Medical removal may be considered along with re-placement in working practices without exposure to WBV. This paper presents opinions on health surveillance for whole-body vibration developed within a working group of partners funded on a European Community Network (BIOMED2 concerted action BMH4-CT98-3251: Research network on detection and prevention of injuries due to occupational vibration exposures). The health surveillance protocol and the draft questionnaire with explanation comments are presented for wider consideration by the science community and others before being considered appropriate for implementation.