Relative Controllability Of Nonlinear Systems Research Articles

Results on relative controllability for nonlinear system with multi‐delays in control

This study uses a delayed matrix exponential to illustrate the solution of both linear and nonlinear delay problems using permutable matrices. We outline several prerequisites that are necessary to ensure the exponential stability of the trivial solution of delay systems. The conditions that are necessary and sufficient for the linear system to possess relative controllability are established by introducing a delayed Grammian matrix‐like criterion. A sufficient condition is obtained by Krasnoselskii's fixed point theorem for the relative controllability of nonlinear systems. Numerical examples provided at the end of the paper demonstrate the validity of our theoretical findings.

Relative null controllability of nonlinear systems with multiple delays in state and control

Sufficient conditions are developed for the relative controllability of nonlinear systems with time-varying multiple delays in the state and control. The results are obtained by defining an appropriate control and its corresponding solution by an integral equation. This equation is then solved using the Schauder's fixed point theorem. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 523-528

Relative controllability of nonlinear systems with multiple delays in state and control

Relative controllability of nonlinear systems with multiple delays in state and control

Relative controllability of nonlinear systems with delays in state and control

In this work, sufficient conditions are developed for the relative controllability of perturbed nonlinear systems with time varying multiple delays in control with the perturbation function having implicit derivative with delays depending on both state and control variable, using Darbo's fixed points theorem. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 239-246

An application of Darbo\'s fixed point theorem in the relative controllability of non-linear systems

Sufficient conditions for the relative controllability of a class of nonlinear systems with distributed delays in the control are established. Our results are based on the measure of non-compactness of a set and the Darbo's fixed point theorem.Global Jouranl of Mathematical Sciences Vol. 6 (1) 2007: pp. 21-26

Global relative controllability of non-linear systems with time-varying multiple delays in control

Sufficient conditions for global relative controllability of non-linear systems with time-varying multiple delays in control and implicit derivatives are derived. The results are obtained using the measure of non-compactness of a set and Darbo's fixed-point principle.

Relative controllability of non-linear systems with distributed delays in control

Abstract Relative controllability of non-linear time-varying systems with distributed delays in the control is considered. Using Schauder's fixed-point theorem, sufficient conditions for global relative controllability are given. The results obtained are a generalization of the results given by Davison and Ball (1972), Davison and Kunze (1970) and Klamka (1975 c, 1976 a, b).