Discrete-time IDA-PBC design for underactuated Hamiltonian control systems

We develop a discrete-time counterpart of IDA-PBC design for a class of Hamiltonian systems. Euler approximate models are used to obtain discrete-time control laws, which are constructed using the coordinate increment discrete gradient. This approach results in a type of discrete-time controller that can be seen as a simple modification of an emulation controller obtained by sample and hold of the continuous-time IDA-PBC controller. However, this simple modification provides a solution to the crucial problem of Hamiltonian conservation. In addition, due to the extra flexibility possessed by the proposed discrete-time IDA-PBC design, it has the capacity that yields a significant improvement to the performance of the sampled-data control system