In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.
Abstract. A controller gain design problem of two-dimensional (2-D) linear systems is proposed in this paper. For one-dimensional (1-D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the feedback gain is given by [1]. Based on the existing 1-D analytical solution, a 2-D state feedback controller gain can be designed to achieve the desired poles. Finally, two numerical examples are shown to exhibit the validity of the proposed approach.
Abstract
In the paper an approximate model of time-varying linear systems using a sequence of time-invariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with time-varying coefficients, namely analytical solution of the Kolmogorov equations is shown.
Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations