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It is known that discrete-time controllers, whose state matrices have no non-integer element, are beneficial in homomorphic based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this note, we investigate the problem from a non-minimality perspective. It is shown that non-minimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with BIBO stable controllers, this framework cannot preserve internal stability. But, benefiting from the... 

This paper presents a method for nonlinear aeroelastic analysis of Human Powered Aircraft (HPA) wings. In this type of aircraft there is a long, highly flexible wing. Wing flexibility, coupled with long wing span can lead to large deflections during normal flight operation; therefore, a wing in vertical and torsional motion using the second-order form of nonlinear general flexible Euler-Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic theory based on Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulations yields the nonlinear integro-differentials aeroelastic equations. Using the Galerkin's... 

The eigenvalue perturbation theorem is used to propose a convex fragility criterion with application to control system design. The criterion can be considered as a non-normality measure of the controller state-space matrix. Non-normality of a matrix is defined as its distance to the nearest real normal matrix within a convex normal subspace. Based on the criterion, an H∞ method for the order reduction of linear time-invariant (LTI) controllers is developed which leads to non-fragile reduced order controllers. 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission  

Denoising is an important preprocessing stage in some Electroencephalography (EEG) applications such as epileptic source localization. In this paper, we propose a new algorithm for denoising the interictal EEG data. The proposed algorithm is based on Generalized Eigenvalue Decomposition of two covariance matrices of the observations. Since one of these matrices is related to the spike durations, we should estimate the occurrence time of the spike peaks and the exact spike durations. To this end, we propose a spike detection algorithm which is based on the available spike detection methods. The comparison of the results of the proposed algorithm with the results of two well-known ICA... 

Least squares estimation is a widely-used technique for range-based source localization, which obtains the most probable position of mobile station. These methods cannot provide desirable accuracy in the case with a non line of sight (NLOS) path between mobile station and base stations. To circumvent this drawback, many algorithms have been proposed to identify and mitigate this error; however, they have a large run-time overhead. On the other hand, new positioning systems utilize a large set of base stations, and a practical algorithm should be fast enough to deal with them. In this paper, we propose a novel algorithm based on subspace method to identify and eliminate the NLOS error.... 

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simplified and a pair of basis functions are found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples  

In the present study, the neutron noise, i.e. The stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The... 

In this paper, we consider the problem of spectrum sensing by using multiple antenna in cognitive radios when the noise and the primary user signal are assumed as independent complex zero-mean Gaussian random signals. The optimal multiple antenna spectrum sensing detector needs to know the channel gains, noise variance, and primary user signal variance. In practice some or all of these parameters may be unknown, so we derive the Generalized Likelihood Ratio (GLR) detectors under these circumstances. The proposed GLR detector, in which all the parameters are unknown, is a blind and invariant detector with a low computational complexity. We also analytically compute the missed detection and... 

In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending–torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the... 

In this letter, we propose the application of the generalized eigenvalue decomposition for the decomposition of multichannel electrocardiogram (ECG) recordings. The proposed method uses a modified version of a previously presented measure of periodicity and a phase-wrapping of the RR-interval, for extracting the "most periodic" linear mixtures of a recorded dataset. It is shown that the method is an improved extension of conventional source separation techniques, specifically customized for ECG signals. The method is therefore of special interest for the decomposition and compression of multichannel ECG, and for the removal of maternal ECG artifacts from fetal ECG recordings. © 2006 IEEE  

Integrating high spatial resolution of functional magnetic resonance imaging (fMRI) and high temporal resolution of electroencephalogram (EEG) is promising in simultaneous EEG and fMRI analysis, especially for epileptic patients. The EEG recorded inside an MR scanner is interfered with MR artifacts. In this article, we propose new artifact reduction approaches and compare them with the conventional artifact reduction methods. Our proposed approaches are based on generalized eigenvalue decomposition (GEVD) and median filtering. The proposed methods are applied on experimental simultaneous EEG and fMRI recordings of an epileptic patient. The results show significant improvement over... 

In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method)  

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary... 

The discrete-time quantum walk dynamics can be generated by a time-dependent Hamiltonian, repeatedly switching between the coin and the shift generators. We change the model and consider the case where the Hamiltonian is time-independent, including both the coin and the shift terms in all times. The eigenvalues and the related Bloch vectors for the time-independent Hamiltonian are then compared with the corresponding quantities for the effective Hamiltonian generating the quantum walk dynamics. Restricted to the non-localized initial quantum walk states, we optimize the parameters in the time-independent Hamiltonian such that it generates a dynamics similar to the Hadamard quantum walk. We... 

In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with... 

In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with... 

Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes. These instabilities have an important role in the mixing process. In this work, the linear stability analysis in spatial framework is used to study the stability characteristics of a particle-laden stratified two-layer flow. The effect of parameters such as velocity-to-density thickness ratio, bed slope, viscosity as well as particle size on the stability is considered. A simple iterative method applying the pseudospectral collocation method that employed Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, the flow becomes stable for Richardson... 

Synchronization among a set of networked nodes has attracted much attention in different fields. This paper thoroughly investigates linear formulation of the Kuramoto model, with and without frustration, for an arbitrarily weighted undirected network where all nodes may have different intrinsic frequencies. We develop a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks. We mathematically prove that the eigenvector corresponding to the largest eigenvalue of the network's Laplacian matrix is enough for examining synchrony alignment and that the functionality of this vector depends on the corresponding eigenvalue. Moreover, we prove... 

Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the...