On the functional observers for linear descriptor systems

This paper is concerned with the design of functional observers for linear time-invariant descriptor systems. Contrary to the functional observers considered for the standard systems in Darouach [8], where the order of these observers is equal to the dimension r of the functional to be estimated, in this paper the order can be of dimension different of that of this functional. When this order is equal to the dimension of the functional and the system is in a standard form, the presented design method becomes that of Darouach [8]. It also generalizes the existing results for descriptor systems. The approach is based on the new definition of partial impulse observability. Sufficient conditions for the existence and stability of these observers are given. Continuous time and discrete time systems are considered. Two numerical examples are given to illustrate our approach.