We establish necessary and sufficient conditions for the solvability of nonlinear boundary-value problem in critical case develop a scheme construction solutions this problem. By using Newton–Kantorovich method, we propose new iterative determination to weakly system ordinary differential equations case. As examples application constructed scheme, obtain approximations periodic Duffing Lienard ...

The use of finite-dimensional linear time-invariant controllers for the stabilization of periodic solutions in sinusoidally forced nonlinear systems is investigated. By mixing results concerning absolute stability of nonlinear systems and robustness of linear systems, a linear matrix inequality-based controller synthesis technique is developed. The synthesis algorithm yields the controller maxi...