This paper considers a class of interconnected nonlinear systems where each subsystem, in the absence of coupling, is individually exponentially stable. The cyclic-small-gain theorem is significantly extended in such a way that the interconnected system is proved to be globally exponentially stable, an exponential converging upper bound of state norm is obtained which fully reveals the relations between the gains, the decay rate and the upper bound of the states. The new result is further applied to fault tolerant safe control problem of interconnected nonlinear systems. A fault recoverability condition with respect to safety is established, under which both individual and cooperative fault tolerant safe control strategies are provided under the decentralized control structure. This guarantees that the states are always within a given safe domain in the presence of faults.

本文考虑了一类相互连接的非线性系统，其中每个子系统在没有耦合的情况下都是指数稳定的。循环小增益定理得到了显着扩展，从而证明了相互连接的系统是全局指数稳定的，获得了指数范式收敛的状态范数上限，充分揭示了增益，衰减率和噪声之间的关系。国家的上限。新结果进一步应用于互联非线性系统的容错安全控制问题。建立了关于安全性的故障可恢复性条件，在该条件下，在分散的控制结构下提供了个人和合作的容错安全控制策略。