Related papers: Singular Perturbation Theory for a Finite-Dimensio…

Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…

This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal…

A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…

The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample…

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…

This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state…

In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…

A state feedback controller design is proposed to guarantee stability of a nonuniformly sampled system for arbitrary selections of sampling periods within an interval, assuming the controller can select the sampling period. It is also shown…

In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the…

This paper proposes a feedback linearizing law for single-track dynamic models, allowing the design of a trajectory tracking controller exploiting linear control theory. The main characteristics of this algorithm are its simplicity, its…

We present a novel scheme of carrying out the Lie-transform perturbation for the guiding-center motion, with an aim at addressing directly the problem of singularity which exists intrinsically in the determining equation for the generating…

This paper develops a robust safety-critical control method for nonlinear strictfeedback systems with mismatched disturbances. Using a state transformation and a linear time-varying disturbance observer, the system is converted into a form…

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level,…

The commutators of the Poincar\'e group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

This paper demonstrates that a computer aided perturbation theory can easily be realized by use of a cumulant approach. In contrast to a recent alternative formulation on the basis of Wegner's flow equation method the present approach can…

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…

Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify…

Discrete time crystalline phases have attracted significant theoretical and experimental attention in the last few years. Such systems require a seemingly impossible combination of nonadiabatic driving and a finite-entropy long-time state,…

Many recent advancements in quantum computing leverage strong drives on nonlinear systems for state preparation, signal amplification, or gate operation. However, the interplay within such strongly driven system introduces multi-scale…