Stabilization of Generalized Hamiltonian Systems

Canonical transformation and stabilization of generalized Hamiltonian systems

This paper introduces generalized canonical transformations for generalized Hamiltonian systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems...

Time-varying Stabilization of Hamiltonian Systems via Generalized Canonical Transformations

This paper focuses on the stabilization of port-controlled Hamiltonian systems employing possibly time-varying controllers. At first we refer to the generalized canonical transformation which preserves the structure of Hamiltonian systems and the passivity property that physical systems innately possess. Next we show a general stabilization strategy for port-controlled Hamiltonian systems based...

Canoni al transformation and stabilization of generalized Hamiltonian systems

Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations

This paper is concerned with the stabilization of nonholonomic systems in portcontrolled Hamiltonian formulae based on time-varying generalized canonical transformations. A special class of time-varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized Hamiltonian structure with passivity. Utilizing these...

Generalized Hamiltonian Structures for Ermakov Systems

We construct Poisson structures for Ermakov systems, using the Er-makov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations...