Nonnegative Consensus Tracking of Networked Systems With Convergence Rate Optimization

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies.