Boundary Control Systems and the System Node

Abstract

In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operatorwhere X is the state space and Y is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems. Copyright

Port Representations of the Telegrapher's Equations

“…Thus, from Theorem 6 and equation 23 where S 2 satisfies S −T 2 S −1 2 = 4I. In (Villegas et al, 2005) it is shown that a system described by the telegrapher's equations with this type of input and output is exponentially stable.…”

“…In this section we show how to represent the telegrapher's equations as a system node. To do this we first need some results, which are taken from (Villegas et al, 2005).…”

Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems

“…systems of the form (1)- (2), have been investigated recently, e.g. in [19,16,6,29,33,30]. Well-posedness and uniform exponential (or, asymptotic) stability for autonomous port-Hamiltonian systems can in most cases be tested via a simple matrix condition [16,15].…”

Une étude sur les spécificités de la commande dans le micromonde

“…Revenons à l'exemple de la poutre d'Euler Bernouilli. L'expression de l'énergie totale du système est donnée par la somme de l'énergie cinétique et de l'énergie potentielle élastique : , la commandabilité, la stabilité (Villegas et al, 2005) etc. peuvent être étudiés en fonction du choix des conditions frontières (telle que (2) par exemple) en utilisant la théorie des semigroupes (Curtain et al, 2005).…”