Stability Criteria Based on Estimates of Dissipation

摘要

Multidimensional nonlinear dynamical systems described by a system of vector-matrix integral equations are considered. Technique of dissipativness estimation, that uses some estimates of integrals, is proposed. Initial estimates of dissipativness are specified by construction of an iterative procedure. Convergence and asymptotics of such iterations are studied. The criteria of asymptotic stability are received as conditions of convergence of a proposed iterative procedure to the zero-estimate of dissipativness.