Energy Shaping of Distributed Port‐Hamiltonian Systems Based on Finite Volume Approximation

ABSTRACT This work introduces a semi‐discrete formulation for a class of infinite‐dimensional port‐Hamiltonian systems (PHS) through a finite volume approach. After spatial discretization, the resulting models maintain the core structural properties of PHS, including the underlying Dirac structure, which is preserved in the absence of external interconnections. A key aspect of this approach involves the integration of a finite‐dimensional controller with the infinite‐dimensional system through a power‐conserving interconnection. Furthermore, we establish a criterion for the existence of discrete analogs of Casimir functions in the discretized framework. The methodology is illustrated through its application to the Timoshenko beam model, where a discrete Casimir function is effectively constructed, reflecting the essential features of the continuous case.