A state space interpretation of simultaneous observation for linear systems

The problem of simultaneously observing two or more LTI systems is considered. Obvious necessary conditions are derived using distinguishability concepts. In this way the existence of a common observer for two systems is related to the existence of an unknown input observer for the parallel system, formed by the difference of the systems. These conditions are also shown to be suf£cient for constructing a common observer, and a structure for such observers is proposed. The use of a special normal form allows to easily check if the conditions are satis-£ed and to effectively construct a family of common observers. Similar conditions are derived for the case of more than two plants. In this case it is shown that the solution of the simultaneous observation problem for N plants can be reduced to the simultaneous observation problem of N − 1 plants, but with unknown inputs. This latter problem is of a higher level of dif-£culty but in a lower number systems, and has not been solved yet (for N > 2).