Discrete-Time IDA-PBC Design For Separable Hamiltonian Systems

We develop a discrete-time counterpart of IDA-PBC design for separable Hamiltonian systems. Euler approximate models are used to obtain the discrete-time control laws, by replacing “differential” in the continuous-time design with “difference” in the discrete-time design. 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, due to the crucial issue of Hamiltonian conservation in IDA-PBC design, this simple modification, which results in an “almost” Hamiltonian conservation in discrete-time, yields a significant improvement to the performance of the sampled-data control system.