We consider an inverse problem of determining a coefficient matrix and an initial value for a first order hyperbolic system. Assuming that the boundary values over a time interval are known, we characterize coefficient matrices and initial values, and prove the uniqueness of some components of the matrix function. The proof is based on a transformation formula and the spectral properties of the...

The Kalman-Yakubovich-Popov lemma is a central result in systems and control theory which relates the positive semidefiniteness of a Popov function on the imaginary axis to the solvability of a linear matrix inequality. In this paper we prove sufficient conditions for the existence of a nonpositive solution to this inequality for differential-algebraic systems. Our conditions are given in terms...

where Y, Z, Kix) and G(x) are « x n matrices and each of Kix) and G(x) is a symmetric matrix of continuous functions on a z% x < oo. By a solution of (b) we mean a pair of n x n matrices {T(x),Z(x)} such that each of the elements of Y and Z is a differentiable function and such that {Y,Z} satisfies the initial condition and satisfies the matrix differential system almost everywhere on a S! x < ...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

This paper presents the non-linear generalization of a previous work on matrix differential models [1]. It focusses on the construction of approximate solutions of first-order matrix differential equations Y ′ (x) = f (x,Y (x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix diff...

Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as b...