Robust disturbance attenuation in Hamiltonian systems via direct digital control

The discrete-time robust disturbance attenuation problem for n-dof mechanical system with energy function uncertainty is considered. First, it is shown that the robust control problem of the n-dof mechanical systems can be reduced to the disturbance attenuation problem when a specific type of control rule is used. Then, the solution of robust disturbance attenuation problem via direct-discrete time design is given as a sufficient condition. Furthermore, a new method is presented using Quadratic Approximation Lemma to construct a discrete gradient of a general energy function. The proposed direct discrete-time design method is used to solve the robust disturbance attenuation problem for the double pendulum system. The simulation results are given for the discrete-gradient obtained with the method presented here.