Controllability and Observability of Parabolic Systems—An Addendum to Two Recent Papers of Y. Sakawa

In two recent articles Sakawa has established necessary and sufficient conditions to insure the controllability (observability) of parabolic systems of finite multiplicity m. One of these conditions is that there must be at least m controllers (sensors). In this short note it is shown that the results of Sakawa can be extended to the case where only one discrete scanning controller (sensor) is used. In some special cases Sakawa’s results can be utilized to establish the observability of a system when only one time-varying sensor is used.