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设τ≥0是系统的非线性反馈f(σ(t-τ))中的时滞,G(iω)是系统线性部分的频率特性。本文证明:非线性控制系统对τ≥0都h-绝对稳定的充分必要条件是,当f(σ)=hσ时的线性系统对τ≥0都渐近稳定或h|G(iω)|<1。
Let τ≥0 be the delay in the system’s nonlinear feedback f (σ (t-τ)), where G (iω) is the frequency characteristic of the linear part of the system. This paper proves that the necessary and sufficient condition for the nonlinear stability of a nonlinear control system over τ ≥ 0 is that the linear system is asymptotically stable for τ ≥ 0 or h | G (iω) | < 1.