One input control and synchronization for generalized Lorenzlike systems

Abstract

This \u00a0paper \u00a0proposes \u00a0a \u00a0new \u00a0class \u00a0of \u00a0nonlinear \u00a0systems \u00a0called \u00a0generalized \u00a0Lorenz-like \u00a0systems which \u00a0can \u00a0be \u00a0used \u00a0to \u00a0describe \u00a0many \u00a0usual \u00a0three-dimensional \u00a0chaotic \u00a0systems \u00a0such \u00a0as \u00a0Lorenz \u00a0system, \u00a0L\u00fc system, \u00a0Chen \u00a0system, \u00a0Liu \u00a0system, \u00a0etc. \u00a0Then \u00a0the \u00a0control \u00a0and \u00a0synchronization \u00a0problems \u00a0for \u00a0generalized Lorenz-like system via a single input are studied and two control laws are proposed based on partial feedback linearization \u00a0with \u00a0asymptotically \u00a0stable \u00a0zero \u00a0dynamics. \u00a0Finally, \u00a0the \u00a0numerical \u00a0simulations \u00a0demonstrate \u00a0the correctness and effectiveness of the proposed control strategies.