Unknown-input state observers with minimal order for linear impulsive systems

This paper deals with the problem of asymptotically estimating a linear function of the state of a linear impulsive system, in the presence of unknown inputs, by means of an observer whose state space has the minimal possible dimension. The linear impulsive systems considered are subject to the following constraint: the length of the time interval between any two consecutive jumps must be greater than or equal to a given finite positive constant. First, a necessary and sufficient condition for the existence of an observer whose state space has a generic dimension (i.e., not necessarily minimal) is proven. Then, the issue of the minimization of the observer state dimension is investigated and solved.