We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC...

The issues of constructing a discrete-time model for Hamiltonian systems are in general different from those for dissipative systems. We propose an algorithm for constructing an approximate discrete-time model, which guarantees Hamiltonian conservation. We show that the algorithm also preserves, in a weaker sense, the losslessness property of a class of port-controlled Hamiltonian systems. An a...

We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not invertible. In addition, we show the eigenstructure and the symplectic properties of the mixed direction nonlinear Hamiltonian dynamics. We extend the Local Stable M...

In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (1) the discrete nonlinear Schrödinger equation, a discrete mean-field theory, and (2) the BoseHubbard Hamiltonian, a discrete quantum-field theory. The former is recovered from the latter in the limit of a product of local coherent states. Using...

a memory control for t-s fuzzy discrete-time systems with sto- chastic input delay is proposed in this paper. dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis- tribution. a new state space model of the discrete-time t-s fuzzy system is derived by introducing some stocha...

Classical Newtonian dynamics is analytic and the energy of an isolated system is conserved. The energy of such a system, obtained by the discrete "Verlet" algorithm commonly used in molecular dynamics simulations, fluctuates but is conserved in the mean. This is explained by the existence of a "shadow Hamiltonian" H [S. Toxvaerd, Phys. Rev. E 50, 2271 (1994)], i.e., a Hamiltonian close to the o...