Controller Design using Extension for Nonlinear Time-varying Systems

Inclusion and extension principles are defined for nonlinear time-varying (NLTV) systems. Contractibility of dynamic NLTV controllers is also discussed and overlapping decompositions and controller design using overlapping decompositions are also presented. The approach involves first expanding an overlappingly decomposed NLTV system such that the expanded system is an extension of the original system. Since the subsystems of the expanded system appear as disjoint, a local controller can easily be designed for each subsystem. These local controllers form a decentralized controller for the overall expanded system. This overall controller can then be contracted for implementation on the original system. It is shown that, if the controller for the expanded system is designed to stabilize the expanded system, then the contracted controller stabilizes the original system.