Stability Analysis of Linear Sylvester System of First Order Differential Equations

In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

Modal waves in multiconductor transmission lines by using fundamental matrix response

The differential equations that model voltage and current for a multiconductor transmission line are written in matrix form. Supposing a time exponential solution through of the modal analysis the modal waves are obtained and solution of a ordinary matrix differential equation, thus determining the amplitude for voltage and current. The modal waves are given in terms of the fundamental matrix solution associated to the ordinary matrix differential equation. The decomposition of the modal waves in forward and backward propagators are used for determine the reflection and transmission matrices for junction in transmission lines. Circulant symmetric transmission lines are discussed, case in that the values for the self-impedance are the same as well as the mutual-impedance values and the same considerations to the admittance matrix. In particular, for these transmission lines are characterized the propagation constants and is observed that the number of multiconductors has effects only on a specific propagation constant. Numerical example of one multiconductor transmission line is presented allowing to observe important aspects of the methodology developed.

Output Control by Linear Time-Varying Systems using Parametric Identification Methods

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour

In the present article, we introduce the second Kummer function with matrix parameters and examine its asymptotic behaviour relying on the residue theorem. Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function.

On ψ Bounded Solutions for a Nonlinear Lyapunov Matrix Differential Equation on 𝕉

Using Banach and Schauder - Tychono fixed point theorems, existence results for a nonlinear Lyapunov matrix differential equation on 𝕉 are given. The obtained results generalize and extend the results from [5] and [18].

Thermal Disturbances in Twinned Orthotropic Thermoelastic Material

This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.