Extension Principle and Controller Design for Nonlinear Systems

We generalize the principle of extension and controller design using this principle for nonlinear systems. We first define principles of inclusion and extension for nonlinear time-invariant (NLTI) systems. Thereafter, we present the necessary and sufficient conditions for a system to be an extension of another and show that when the expanded system is an extension of the original system, any controller designed for the expanded system can be contracted for implementation on the original system. Subsequently, we demonstrate how an overlappingly decomposed NLTI system can be expanded so that the expanded system is an extension of the original system, how decentralized controllers can be designed for the expanded system, and how these controllers can be contracted for implementation on the original system. An example is also provided to illustrate the extension and contraction concepts and show controller design using the proposed principles.