Disturbance Attenuation in Hamiltonian Systems via Direct Discrete-Time Design

The discrete-time disturbance attenuation problem for a class of Hamiltonian systems is considered. In order to give a sufficient condition for the solution of the considered problem, firstly an appropriate discrete gradient is proposed, which enables the derivation of the discrete time version of the given Hamiltonian systems. The disturbance attenuation problem characterised by means of L2 gain is redefined in the discrete-time setting. The proposed direct discrete-time design method is used to solve the disturbance attenuation problem for the double pendulum system in simulations.