Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation

In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions can be easily constructed. Interestingly enough, for linear systems the resulting Lyapunov function is the incremental energy; thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are give

Putting energy back in control

A control system design technique using the principle of energy balancing was analyzed. Passivity-based control (PBC) techniques were used to analyze complex systems by decomposing them into simpler sub systems, which upon interconnection and total energy addition were helpful in determining the overall system behavior. An attempt to identify physical obstacles that hampered the use of PBC in applications other than mechanical systems was carried out. The technique was applicable to systems which were stabilized with passive controllers

Boundary control for a class of dissipative differential operators including diffusion systems

In this paper we study a class of partial differential equations (PDE's), which includes Sturm-Liouville systems and diffusion equations. From this class of PDE's we define systems with control and observation through the boundary of the spatial domain. That is, we describe how to select boundary conditions, such that the resulting system has inputs and outputs acting through the boundary. Furthermore, these boundary conditions are chosen in a way that the resulting system has a nonincreasing energy.\u

Utilization of Birefringent Fiber as Sensor of Temperature Field Disturbance

The paper deals with utilization of induced birefringence sensitivity to temperature field in birefringent optical fibers. The propagating optical wave and optical fibers are described by means of coherency and Jones matrices, which are decomposed into unitary matrix and spin matrices. The development of polarization caused by temperature field is interpreted on the Poincare sphere by means of MATLAB® environment. The temperature sensitivity of Panda and bow-tie fiber has been measured for circular polarization excitation. Curves of intensity fluctuation caused by the temperature dependence are presented

Interaction-assisted propagation of Coulomb-correlated electron-hole pairs in disordered semiconductors

A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair.Comment: 4 pages and 3 ps figure

Off-diagonal disorder in the Anderson model of localization

We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition (MIT) as a function of diagonal disorder, as well as its energy dependence. Furthermore we investigate the different influence of odd and even system sizes on the localization properties in quasi one-dimensional systems. Applying the finite-size scaling approach in conjunction with a nonlinear fitting procedure yields the critical parameters of the MIT. In three dimensions, we find that the resulting critical exponent of the localization length agrees with the exponent for the Anderson model with pure diagonal disorder.Comment: 12 pages including 4 EPS figures, accepted for publication in phys. stat. sol. (b

Port-Hamiltonian systems on graphs

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and internal vertices. This allows for state variables associated to the edges, and formalizes the interconnection of networks. Examples from different origins such as consensus algorithms are shown to share the same structure. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis of the resulting dynamics.Comment: 45 pages, 2 figure