Decentralized estimation and control with overlapping input, state, and output decomposition

Abstract The extension principle, which was introduced recently, is generalized to the case of input, state, and output expansion. Estimator and controller design problems are considered within the framework of the extension principle. Decentralized estimator and controller design with overlapping decompositions is also discussed within the same framework. It is shown that if the extension principle is used then any estimator or controller designed in the expanded spaces is contractible to the original spaces for implementation. Furthermore, it is shown that if an estimator designed for the expanded system achieves good estimation and/or asymptotic estimation then the contracted estimator also achieves good estimation and/or asymptotic estimation for the original system. Similarly, it is also shown that if a controller designed for the expanded system achieves stability and/or good performance then the contracted controller achieves stability and/or good performance for the original system.