On The Ψ – Asymptotic Stability Of Nonlinear Lyapunov Matrix Differential Equations

Abstract

In this paper are proved (necessary and) sufficient conditions for Ψ− asymptotic stability of the trivial solution of nonlinear Lyapunov matrix differential equations.

On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

“…From Lemma 2.8, we know that the matrix U (t) = Y T (t) ⊗ X(t) is a fundamental matrix for the linear homogeneous system associated with (6), i.e. for the differential system (8).…”

On the Ψ - Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

“…The important properties and rules of calculation of the vectorization operator there are in Lemmas 2 -4, [5].…”

“…Remark 2.1. The definitions of various types of Ψ− stability on R + for a vector differential equation (6) was given in [5], [6], [7].…”

“…Recent results for Ψ− boundedness, Ψ− stability, Ψ− instability, dichotomy and conditioning for Lyapunov matrix differential equations have been given in many papers. See, for example, [4], [5], [6], [8], [9], [11].…”

On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations

“…In our papers [6], [7], [8] are proved (necessary and) sufficient conditions for Ψ-(uniform) stability, Ψ-asymptotic stability and Ψ-instability of the trivial solutions of (nonlinear) Lyapunov matrix differential equations (1.1), (1.2) and (1.3).…”