Stability of Distributed Heterogenous Systems with Static Nonlinear Interconnections

The paper studies the problem of L₂ stability of distributed heterogenous systems with static nonlinear interconnection structures. Under the assumptions that the nodes of the network are the single input single output operators defined on the finite square integrable space, and that the nodes are interconnected by the time-varying static nonlinearities that satisfies the sector condition. For such constructed distributed heterogenous systems, the algebraic quadratic condition that is satisfies by the interconnection mapping of the network is established first. Based on this, under the assumption that the interconnection of the network is well-posed, the condition that the network is of finite gain L₂ stability is presented. Further more, when the dynamics of the nodes are described by linear time invariant operators, the frequency domain condition that insures the finite gain L₂ stability of the network is put forward.