A new bound for the condition number of the matrix exponential is presented. Using the bound, we propose an efficient approximation to the condition number, denoted by κg(s,X), that avoids the computation of the Fréchet derivative of the matrix exponential that underlies condition number estimation in the existing algorithms. We exploit the identity eX = (eX/2 s )2 s for a nonnegative integer s...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

The analysis of practical queueing problems benefits if realistic distributions can be used as parameters. Phase type (PH) distributions can approximate many distributions arising in practice, but their practical applicability has always been limited when they are described by a non-Markovian vector-matrix pair. In this case it is hard to check whether the non-Markovian vector-matrix pair defin...

The robust exponential stability is investigated for a class of uncertain neutral-type neural networks with discrete and distributed time-varying delays. By introducing a new vector Lyapunov-Krasovskii functional, using Jensen integral inequality, free-weighting matrix method and linear matrix inequality techniques, delay-dependent sufficient conditions are obtained for exponential stability of...

The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for matrix exponential computation. It uses forward and backward error analysis with improved bounds for normal and nonnormal matrices. Applied to the Taylor method, it has presented a lower or similar cost compared to the st...

The pseudospectra of banded finite dimensional Toeplitz matrices rapidly converge to the pseudospectra of the corresponding infinite dimensional operator. This exponential convergence makes a compelling case for analyzing pseudospectra of such Toeplitz matrices—not just eigenvalues. What if the matrix is dense and its symbol has a jump discontinuity? The pseudospectra of the finite matrices sti...

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...

The feedback synthesis of linear systems satisfying certain exponential bounds on their transient behavior is studied. We present sufficient conditions ensuring that there exists a state feedback matrix such that the closed loop system satisfies a desired exponential growth bound. Special interest is directed to the case of generating contraction semigroups, which under certain conditions can b...

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are deriv...

Abstract: In this paper, the global exponential stability of BAM neural networks with inertial term and time delay are investigated. By chosen proper variable substitution the system is transformed to f rst order differential equation. Then some new suff cient conditions, which can ensure the globally exponential stability of the system are obtained by constructing suitable Lyapunov functional,...