Partial equiasymptotic stability of nonlinear dynamic systems

Abstract

For nonlinear nonautonomous dynamic systems, partial equiasymptotic stability of the zero equilibrium position, equiasymptotic stability of the "partial" equilibrium position, and partial equiasymptotic stability of the "partial" equilibrium position are studied by the Lyapunov functions method. Examples are given.

Partial stability and control: The state-of-the-art and development prospects

“…Thus Lyapunov functions of a wider class were found to be helpful in studying partial stability: they, in general, are not sign definite in the Lyapunov-Rumyantsev sense, their derivatives may even be sign-alternating in domains (2.3) and (2.8). This considerably widens the bounds of application of the Lyapunov functions method in studying partial stability [23,319,26,28,29,4].…”

“…-partial stability under arbitrary or large initial perturbations of the "noncontrollable" part of variables [278,120,21,319,29], -partial equiasymptotic stability, which is an intermediate between partial asymptotic stability and uniform partial asymptotic stability [266,120,48,4], and -quasistability of "partial" equilibrium positions [28,29,31] (see Definitions 4 and 6).…”

“…Conditions for such a kind of stability have been obtained for the Lyapunov functions method [29,4].…”

“…Unified solvability conditions for different classes of problems of partial asymptotic stability, equiasymptotic stability, and uniform asymptotic stability are derived in [28,29,31,4].…”