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We investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor…
This paper presents a controller design and optimization framework for nonlinear dynamic systems to track a given reference signal in the presence of disturbances when the task is repeated over a finite-time interval. This novel framework…
We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
A synoptic review of the electrical circuital model-based analysis of laboratory plasma sheaths, alongside their stability features in a realistic broader horizon, is systematically presented herein. It explains the basic physics…
An electronic circuit realization of the logistic difference equation is presented using analog electronics. The behavior of the realized system is evaluated against computer simulations of the same. The circuit is found to exhibit the…
Given the intrinsic nonequilibrium nature of high-energy collisions the investigation of the dynamical properties of transport phenomena is important. The study of the real-time behavior of various conductivities and susceptibilities help…
A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the…
Neural networks have demonstrated remarkable success in modeling nonlinear dynamical systems. However, identifying these systems from closed-loop experimental data remains a challenge due to the correlations induced by the feedback loop.…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic…
A nonlinear dynamics of the thermal and electromagnetic instability of critical state in type II superconductors has been analysed taking into account effects of dissipation and dispersion. An existance of a nonlinear running waves…
I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge…
The argument of physical dimension/units is applied to electrical switched circuits, making the topic of the nonlinearity of such circuits simpler. This approach is seen against the background of a more general outlook (IEEE CAS MAG, III,…
We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges…
Quasi-static protocols for systems that feature a mixed phase-space with both chaos and quasi-regular regions are beyond the standard paradigm of adiabatic processes. We focus on a many-body system of atoms that are described by the…