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Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems

Yasuaki Hiraoka (2007)

Kybernetika

We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.

Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point

Antonio Giorgilli (1988)

Annales de l'I.H.P. Physique théorique

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Chao Sun, Fuli Wang, Xiqin He (2016)

Open Mathematics

This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered...

Robustness of decentralized control subject to nonlinear perturbation in the system dynamics

Djordjija B. Petkovski (1984)

Kybernetika

Roughness of $(μ_{1}, μ_{2})$ -dichotomies under small perturbations in $L^{\infty}$ .

Lizana, Marcos (1998)

Divulgaciones Matemáticas