Fixed-Order H-Infinity Controller Design for Port-Hamiltonian Systems

The paper proves that the negative-feedback interconnection of two pH systems is Lyapunov stable by converting the closed loop to a dissipative Hamiltonian pencil and invoking an external theorem; this yields eigenvalues in the closed left-half plane with semisimple imaginary-axis eigenvalues (Proposition 1 and its proof) . The candidate solution proves the same statement via a direct passivity/energy argument, constructing a quadratic Lyapunov inequality for the closed-loop ODE under standard well-posedness of the algebraic loop. The two arguments are logically consistent and reach the same conclusion; the model’s proof assumes invertibility of the feedthrough interconnection (well-posedness), whereas the paper sidesteps this by working with a descriptor-pencil representation and explaining the role of the added infinite eigenvalues . Both are correct; the proofs are different in method.