Stability analysis for a class of Hamiltonian systems with digital control

On contrast to the successful achievement of nonlinear control theory with continuous-time feedback as in, e.g., there are less studies on the digital control of nonlinear systems with notable exceptions, e.g. In particular there are few results on quantitative aspects of the subject. This article considers a digital implementation problem of the passivity based control for port-controlled Hamiltonian systems. A sufficient condition for asymptotic stability is given in terms of the Hamilton-Jacobi-Isaac inequality. A more tractable sufficient condition is also shown with a reward of conservatism. The effectiveness of the proposed methods is demonstrated by numerical examples.