Exponential small-gain theorem and fault tolerant safe control of interconnected nonlinear systems

Abstract

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.