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., [1], [5], there are less studies on the digital control of nonlinear systems with notable exceptions, e.g., [2], [4]. 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.