Related papers: Singular Perturbation Theory for a Finite-Dimensio…
We consider Bloch states of weak spacetime-periodic perturbations of homogeneous materials in one spatial dimension. The interplay of space- and time-periodicity leads to an infinitely degenerate dispersion relation in the free case. We…
It is shown that an account for combined effect of both nonmagnetic and magnetic scatterers on Tc and/or an assumption about a non-pure d-wave order parameter allows for a quantitative explanation of the experimental data on the electron…
We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…
Recently developed control methods with strong disturbance rejection capabilities provide a useful option for control design. The key lies in a general concept of disturbance and effective ways to estimate and compensate the disturbance.…
In response to the continuously changing feedstock supply and market demand for products with different specifications, the processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve the…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
We present an approach for the calculation of the $\mathbb{Z}_2$ topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline…
I present an outline of chiral perturbation theory and discuss some recent developments in the field.
The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the…
We analyze earlier applications of perturbation theory by the moment method (also called inner product method) to anharmonic oscillators. For concreteness we focus on two-dimensional models with symmetry $C_{4v}$ and $C_{2v}$ and reveal the…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a…
We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines…
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which…
In this paper we analyze one-matrix models by means of the associated discrete linear systems. We see that the consistency conditions of the discrete linear system lead to the Virasoro constraints. The linear system is endowed with gauge…
We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…