Related papers: Exact eigenvalue assignment of linear scalar syste…
This work deals with the interior transmission eigenvalue problem: $y'' + {k^2}\eta \left( r \right)y = 0$ with boundary conditions ${y\left( 0 \right) = 0 = y'\left( 1 \right)\frac{{\sin k}}{k} - y\left( 1 \right)\cos k},$ where the…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
We complete the first step towards the resolution of several decades-old challenges in disturbance-robust adaptive control. For a scalar linear system with an unknown parameter for which no a priori bound is given, with a disturbance that…
In this paper we present a decentralized algorithm to estimate the eigenvalues of the Laplacian matrix that encodes the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The basic idea is…
The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…
We consider the eigenvalue problem $Ax = \lambda x$ where $A \in \mathbb{R}^{n \times n}$ and the eigenvalue is also real $\lambda \in \mathbb{R}$. If we are given $A$, $\lambda$ and, additionally, the absolute value of the entries of $x$…
In this paper, inequalities among eigenvalues of different self-adjoint discrete Sturm-Liouville problems are established. For a fixed discrete Sturm-Liouville equation, inequalities among eigenvalues for different boundary conditions are…
Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accuracy, extracting an approximate eigenpair…
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…
We provide two solutions to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. Both of our solutions are global, employ the…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
Abel's classic transformation shows that any well-posed system with time-varying delay is equivalent to a parameter-varying system with fixed delay. The existence of such a parameter-varying constant delay representation then simplifies the…
In this paper, we study the dynamical behavior of a linear control system on $\R^2$ when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
In this study, we consider a boundary value problem generated by the Sturm-Liouville problem with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and characteristic function…