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We consider a class of first order linear differential equations given in infinite-dimensional space. We study asymptotic behavior of individual solutions in the context of stability. In particular, we are looking for the slowest decaying solution, that is maximal asymptotic. We present some new result on nonexistence of maximal asymptotics for certain class of linear equations.
The paper presents analysis of behavior of rotating Timoshenko beam-disk-spring system whose movement is controlled by angular acceleration of the driving motor into which the beam is dissipatively clamped. We present analytical formulas for the location of spectrum of the system.
A model of elastic-coupled strings subjected to external control is considered, and the spectral properties of its operator model are presented. The problem of reachable states description is explored and solved in the form of convergence of series connected with final states.
The computational costs of the parameter space approach, which is used to calculate the stability boundaries for linear time-invariant systems (LTI), increase fast with the dimension of the investigated system. In this paper, the authors present a successive approximation of the stability boundaries for large scale systems. The approximation provides a fast and accurate estimation of the stability...
The paper considers the class of discrete-time, single-input, single-output, nonlinear dynamical systems described by a polynomial difference equation. This class, call polynomial time-invariant, is a proper generalization of the linear time-invariant model class. The identification data is assumed to be generated in the errors-in-variables setting, where the input and the output noise is zero mean,...
In this article, a new method for numerical solution of eigenproblems for linear Hamiltonian systems is presented. It is applied to calculation of natural frequencies of rod-like systems with distributed parameters. Three widely used models (Euler-Bernoulli, Rayleigh and Timoshenko) for transverse vibrations of a rod with hinged ends are considered alongside with a pipeline vibration model. The results...
We consider a semi-infinite Jacobi matrix corresponding to the discrete Schrödinger operator with two-dimensional perturbation. Let βk, β l be nonzero diagonal elements of the Jacobi matrix. Our goal is to find the exact condition on the coupling constants βk, βl for which there are no bound states of the Schrödinger equation. In addition, it is proved that the lines bounding the area of allowable...
We consider resonances of fourth order ordinary differential operator with compactly supported coefficients on the line. We determine estimates of the number of resonances in complex discs at large radius and asymptotics of resonances.
We discuss the solution of boundary value problems that arise after the separation of variables in the Schrödinger equation in oblate spheroidal coordinates. The specificity of these boundary value problems is that the singular points of the differential equation are outside the region in which the eigenfunctions are considered. This prevents the construction of eigenfunctions as a convergent series...
A hybrid manifold having the form of bent chain of spheres connected through 1D wires is considered. The discrete spectrum for the Dirac operator is studied. The model is based on the theory of self-adjoint extensions of symmetric operators.
Many calibration algorithms for vector network analyzers using partially unknown standards can be stated as an eigenvalue problem. The construction of the eigenvalue problem is described and examples for line reflect match (LRM) and thru reflect line (TRL) calibrations are given. Advantages of the new algorithm are that all uncertainties can be taken into account and that it is fully analytic. A further...
This work considers a method for including mutual coupling in the characteristic mode analysis (CMA) formulation of finite antenna array elements. The approach applies the domain Green's function method, i.e., a domain decomposition approach based on the method of moments, to extract an active impedance matrix for each array element. These impedance matrices model the active array environment for...
The problem of the analytical synthesis of reduced order state observer for dynamic system, which is exposed to signal and parametric perturbations, has been considered. The conditions under which it is possible to build a nonlinear observer with an estimation error of the state vector, which asymptotically tends to zero, have been formulated. Formulas for calculation the matrix coefficients of the...
Lithium ion batteries are widely used for energy storage. Its capacity degradation modeling and cycle to failure estimation has become very significant. Repeated capacity measurements over the whole life of batteries, i.e., the longitudinal data, are investigated to understand the degradation process and the cycle to failure behavior. This paper proposes a method for prognostics of lithium ion batteries...
The aim of this research work is to analyse sub-synchronous control interaction (SSCI) in doubly-fed induction generators (DFIGs) and to design a supplementary control technique for the mitigation of SSCI. A mathematical model of the DFIG is derived and linearized in order to perform an eigenvalue analysis. This analysis pinpoints the parameters of the system which are sensitive in making sub-synchronous...
This paper deals with the impact of time delays on small-signal stability of power systems with an all converter-interfaced generation. For this purpose, a delay differential algebraic equation model of the voltage source converter and its control scheme is developed. The regulation is based on replicating the dynamical properties of a synchronous machine through appropriate controller configuration...
Load modeling has been extensively studied in power systems. The problem is intrinsically hard, as a simple description is sought for a large collection of heterogeneous physical devices. One aspect of model simplification has to do with the number of parameters needed to describe a dynamic load. With the rich tapestry of methods proposed in the literature as a backdrop, this paper introduces a new...
Although the theoretical aspects of the particle swarm optimization (PSO) seem to be forsaken, the few previous modeling studies —even with some assumptions— enlarged our knowledge of the PSO process. Here, we suggest a new model of PSO where all the N particles of the swarm and their components are considered. The iterative process is formulated by a 3N×3N block triangular matrix and its spectral...
In this paper an algorithm for modal control of linear time-invariant (LTI) discrete system is proposed to improve the quality of the processes and achieve the desired stability degree of the system. For this purpose the suggested algorithm is calculating the feedback state vector for a single-input single-output (SISO) system so that the closed loop poles to be distributed into a predefined sector...
The study focuses on the investigation small-signal stability in power systems using two methods. One of the methods is traditional method of modal analysis investigating behavior of the eigenvalues. Another one is a new sub-Gramians method that was worked out in Institute of Control Sciences (ICS) RAS. The method is based on the application of the so-called sub-Gramians derivable from solving the...
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