Controller Design for Large-scale Nonlinear Time-delay Systems

Overlapping decentralized controller design is considered for large-scale nonlinear time-delay systems (NLTDSs). Principles of inclusion, limitation, and completion are first defined for such systems. It is then shown that limitation and completion are, in fact, special cases of inclusion. Conditions for an NLTDS to be a limitation or completion of another such system are then derived. Four different stability definitions are considered for NLTDSs. It is shown that if a stable (in any one sense considered) NLTDS includes another such system, then the latter system is also stable. It is then shown that if an NLTDS is a limitation of another such system, then reduction of any controller is assured. Furthermore, this reducted controller stabilizes the former system if the original controller stabilizes the latter system. Finally, overlapping decompositions of large-scale NLTDSs are considered.