The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter multiplying the Laplace operator in the Poisson equation). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit and the former can be interpret...

Relaxation oscillations are periodic orbits of multiple time scale dynamical systems that contain both slow and fast segments. The slow-fast decomposition of these orbits is defined in the singular limit. Geometric methods in singular perturbation theory classify degeneracies of these decompositions that occur in generic one parameter families of relaxation oscillations. This paper investigates...

A decentralized model predictive controller applicable for some systems which exhibit different dynamic characteristics in different channels was presented in this paper. These systems can be regarded as combinations of a fast model and a slow model, the response speeds of which are in two-time scale. Because most practical models used for control are obtained in the form of transfer function m...

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimate...

A system of waves coupled by three-wave, or triad, interactions is considered. A model is constructed to describe the response of a single test wave to interaction with a "heat bath" of "ambient waves." An exact solution for the relaxation of the test wave amplitude is obtained. Regimes of validity are shown for the use of a Langevin equation based on a two-time scale perturbation theory.

This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using successive Galerkin approximation(SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using SGA. We...