Uniform Lipschitz and Asymptotic Stability for Perturbed Differential Systems

Abstract

Abstract. In this paper, we investigate uniform Lipschitz and asymptotic stability for perturbed differential systems using integral inequalities.

Uniformly Lipschitz Stability and Asymptotic Property of Perturbed Functional Differential Systems

“…where a, b, c, k ∈ C(R + ), a, b, c, k, w ∈ L 1 (R + ), w ∈ C((0, ∞)), T is a continuous operator, and w(u) is nondecreasing in u, u ≤ w(u), and Remark 3.10. Letting a(t) = 0 in Theorem 3.9, we obtain the same result as that of Corollary 3.4 in [13].…”

“…Letting a(t) = 0 in Theorem 3.1, we obtain the same result as that of Theorem 3.6 in [13]. where a, b, c, k ∈ C(R + ), a, b, c, k, w ∈ L 1 (R + ), w ∈ C((0, ∞)), T is a continuous operator, and w(u) is nondecreasing in u, u ≤ w(u), and Remark 3.10.…”

“…Choi et al [7] examined Lipschitz and exponential asymptotic stability for nonlinear functional systems. Also, Goo [11,12] and Choi and Goo [5,6] and Goo et al [13] investigated Lipschitz and asymptotic stability for perturbed differential systems.…”

Uniformly Lipschitz Stability and Asymptotic Behavior of Perturbed Differential Systems

“…Choi et al [7] studied Lipschitz and exponential asymptotic stability for nonlinear functional systems. Also, Goo [11,12,13] and Choi and Goo [5,6] and Goo et al [14] investigated Lipschitz and asymptotic stability for perturbed differential systems.…”

Lipschitz and Asymptotic Stability of Perturbed Functional Differential Systems

“…Choi et al [6,7] examined Lipschitz and exponential asymptotic stability for nonlinear functional systems. Also, Goo et al [11,13] investigated Lipschitz and asymptotic stability for perturbed differential systems.…”