Dissipativity reinforcement in interconnected systems

This paper focuses on the reinforcement of the quantitative performance in interconnected dynamical systems. The following problem is addressed that concerns dissipativity reinforcement via interconnection: Find a class of subsystems and their interconnection rule such that the L2 gain bound of the entire interconnected system is reduced compared with that of each individual subsystem. We assume that each subsystem has a special passivity property that is characterized by two parameters, and has a bounded L2 gain. Then, the feedback connection and the more general interconnection of the subsystems are expressed by the transition of the two parameters inheriting the same passivity property. In addition, the L2 gain bound of the entire interconnected system, estimated with the parameters, is strictly reduced and becomes less than that of each subsystem. Finally, special interconnection rules are considered to show that the scale-expansion of the interconnected system, i.e., increasing the number of subsystems, gradually reduces the L2 gain bound.