Inputs, outputs and states in the representation of time series

Impulse Controllability: From Descriptor Systems to Higher Order DAEs

“…The construction of a state variable for a behavior can be done through the "state map" X(d/dt): a map that acts on the variable w and gives a state variable x, i.e., x := X(d/dt)w. We focus in this paper on the state map constructed using the "shift-and-cut-procedure" on a polynomial matrix R defining the behavior [23]. See also [16], [18].…”

Why “state” feedback?

“…We proceed to illustrate the concept of state map introduced in Rapisarda et al (1997) (see also Praagman (1988)), and how it relates to the specification of the "initial conditions" of a trajectory by means of a "prefix" trajectory.…”

The Stable Embedding Problem

“…Any behavior, defined by a kernel representation, we can also represent by an observable state space representation (Praagman (1988); Rapisarda and Willems (1997)). Let the behavior be given by…”