Robust Output Feedback Consensus for Networked Identical Nonlinear Negative-Imaginary Systems
Kanghong Shi, Igor G. Vladimirov, Ian R. Petersen
Abstract
A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and also extend the definition of OSNI systems to nonlinear scenarios. Asymptotic stability is proved for the closed-loop interconnection of a nonlinear NI system and a nonlinear OSNI system under reasonable assumptions. Then, an NI property and an OSNI-like property are proved for networked identical nonlinear NI systems and networked identical linear OSNI systems, respectively. Output feedback consensus is proved for a network of identical nonlinear NI plants by investigating the stability of its closed-loop interconnection with a network of linear OSNI controllers. This closed-loop interconnection is proposed as a protocol to deal with the output consensus problem for networked identical nonlinear NI systems and is robust against uncertainty in the individual system’s model.