Analysis of impulsive modes and Luenberger observers for descriptor systems

In this paper, the distinction between impulsive modes that can be generate d by inputs and impulsive modes that can only be generated by initial condi tions is investigated for linear time-invariant descriptor systems. It reve als that the input-generatable impulsive modes are very crucial to the exis tence of normal Luenberger observers of the systems. Based on this observat ion, an earlier known concept called strongly detectability for regular des criptor systems is extended to irregular case that is shown to be of much c learer physical meanings in classical sense than a recently proposed equiva lent notion of causal detectability does. Thus, similar to the regular case , strong detectability is also a sufficient and necessary condition for the existence of normal Luenberger observers of irregular descriptor systems. (C) 2001 Elsevier Science B.V. All rights reserved.