Observer-Based Realization of Control Systems
Abstract
A novel model reduction framework for large-scale complex systems is proposed by introducing function-type dynamic control systems via the dimension-keeping semi-tensor product (DK-STP) of matrices. Utilizing bridge matrices, the DK-STP facilitates the construction of an approximate observer-based realization (OR) of a linear control system in the form of a function-type control system, where the functions serve as observers. A necessary and sufficient condition is established for the OR-system to admit exact observer dynamics. When an exact OR-system does not exist, an extended OR-system is developed by incorporating the original system's observers into its state. Furthermore, a minimal feedback extended OR-system is constructed, and its relationship to Kalman's minimal realization is analyzed. Finally, the proposed approach is extended to nonlinear control-affine systems.
Cite
@article{arxiv.2404.15688,
title = {Observer-Based Realization of Control Systems},
author = {Daizhan Cheng and Xiao Zhang and Zhengping Ji and Changxi Li},
journal= {arXiv preprint arXiv:2404.15688},
year = {2025}
}