Abstract
This paper is concerned with questions regarding observability and state determination on the basis of the measurement data from a finite number of sensors. The questions are studied for distributed-parameter systems described by linear partial differential equations of parabolic type. First, observability is defined and the necessary and sufficient condition for the observability is given. It has become clear that for the observability of the system, at least the same number of sensors is needed as the multiplicity of a differential operator of the partial differential equation.
When we determine the state of the system at t=T on the basis of the measurement data for 0≤t≤T, it is required that the state to be determined should depend continuously on the measurement data. We obtain the sufficient condition for that requirement. Locations of sensors for ensuring the observability and the continuous dependence of the state on the measurement data are discussed for several examples.
