**1.1 Brief summary of this chapter**

This chapter shows that basic boundary control strategies for *magnetohydrodynamics* (MHD) can be derived from a formal system representation, called a *port-Hamiltonian system* (Van der Schaft and Maschke, 2002). The port-Hamiltonian formulation clarifies collocated input/output pairs used for stabilizing and assigning a global stable point. The controls called *passivity-based controls* (Arimoto, 1996; Ortega et al., 1998; Van der Schaft, 2000; Duindam et al., 2009) are simple and robust to disturbances. Moreover, port-Hamiltonian systems can be connected while keeping their consistency with respect to energy flows. Finally, we show that port-Hamiltonian systems can be used for boundary controls. In the future, this theory might be specialized, for instance, in order to control disruptions of Tokamak plasmas (Wesson, 2004; Pironti and Walker, 2005; Ariola and Pironti, 2008). This chapter emphasizes the versatility of control system representations.
