Input-to-state stability (ISS) is considered for a nonlinear “soft-reset” system with inputs. The latter is a system that approximates a hard-reset system, which is modeled as a hybrid system with inputs. In contrast, a soft-reset system is modeled as a differential inclusion with inputs. Lyapunov conditions on the hard-reset system are given that guarantee ISS for the soft-reset system. In turn, it is shown when global asymptotic stability for the origin of the zero-input reset system guarantees ISS for nonzero inputs. Examples are given to demonstrate the theory.

中文翻译：

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具有非线性数据的软复位系统的输入状态稳定性

输入状态稳定性 (ISS) 被考虑用于具有输入的非线性“软复位”系统。后者是一个类似于硬重置系统的系统，它被建模为具有输入的混合系统。相比之下，软复位系统被建模为输入的微分包含。给出了硬复位系统的李亚普诺夫条件，保证了软复位系统的ISS。反过来，它显示了零输入重置系统原点的全局渐近稳定性何时保证非零输入的 ISS。给出了示例来证明该理论。