Abstruct-The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian whitenoise inputs. It is shown that a symmetric state covariance matrix provides the key link between the statespace equations of a system and the system output covariance matrix. Furthermore, s...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and componentwise) and non-linear non-local perturbation bounds ar...

Different from gradient neural networks (GNN), a special kind of recurrent neural networks has been proposed recently by Zhang et al for solving online linear matrix equations with time-varying coefficients. Such recurrent neural networks, designed based on a matrixvalued error-function, could achieve global exponential convergence when solving online time-varying problems in comparison with gr...

AX B In the paper, a class of fuzzy matrix equations    B where A is an m × n crisp matrix and is an m × p arbitrary LR fuzzy numbers matrix, is investigated. We convert the fuzzy matrix equation into two crisp matrix equations. Then the fuzzy approximate solution of the fuzzy matrix equation is obtained by solving two crisp matrix equations. The existence condition of the strong LR fuzzy s...

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

this paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp m-matrix. thefuzzy linear system (fls) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. however, solving this crisp system isdifficult for large n because of dimensionality problems . it is shown that thisdifficulty may be avoide...

Some years ago Kriese and Siewert [1] used an idea of Pahor [2], and Pahor and Larson [3], which can be seen to be closely related to the computational scheme suggested by Shure and Natelson [4], to incorporate the linear constraint into the calculation of the H matrix applicable to the scattering of polarized light. It was found [ 1 ] that for weakly absorbing media, co ~ 1, the developed equa...

This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...