Analysis of impulsive modes and Luenberger observers for descriptor systems

Abstract

In this paper, the distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time-invariant descriptor systems. It reveals that the input-generatable impulsive modes are very crucial to the existence of normal Luenberger observers of the systems. Based on this observation, an earlier known concept called strongly detectability for regular descriptor systems is extended to irregular case that is shown to be of much clearer physical meanings in classical sense than a recently proposed equivalent 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.