摘要：We prove that the system θ ˙ ( t ) = Λ ( t ) θ ( t ) $\dot{\theta}(t) =\Lambda(t)\theta(t)$ , t ∈ R + $t\in\mathbb{R}_{+}$ , is Hyers-Ulam stable if and only if it is uniformly exponentially stable under certain conditions; we take the exact solutions of the Cauchy problem ϕ ˙ ( t ) = Λ ( t ) ϕ ( t ) + e i γ t ξ ( t ) $\dot{\phi}(t)=\Lambda(t)\phi(t)+e^{i\gamma t}\xi(t)$ , t ∈ R + $t\in\mathbb{R}_{+}$ , ϕ ( 0 ) = θ 0 $\phi(0)=\theta_($ as the approximate solutions of θ ˙ ( t ) = Λ ( t ) θ ( t ) $\dot{\theta}(t)=\Lambda(t)\theta(t)$ , where γ is any real number, ξ is a 2-periodic, continuous, and bounded vectorial function with ξ ( 0 ) = 0 $\xi(0)=0$ , and Λ ( t ) $\Lambda(t)$ is a 2-periodic square matrix of order l.
关键词：Hyers-Ulam stability ; uniform exponential stability ; nonautonomous system ; periodic system
