2016/06/10 by Tinashe Chingozha, Chingozha, Tinashe, Otis T. Nyandoro +5
Engineering · Mathematics · Physics and Astronomy · #Adaptive Control of Nonlinear Systems #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1606.03327
openalex publication_date 2016/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of zero dynamics is a cornerstone of many solutions to important control problems such as feedback linearisation and disturbance decoupling. For a SISO affine control system with relative degree strictly less than the order of the system, it is known that there exists a state transformation and a feedback transformation such that the system can be transformed to a linear system. Making use of the fibre bundle structure induced by the state transformation we show that it is possible to define a connection on the state manifold such that the zero dynamics can be defined as a vertical vector field. In this formalism the zero dynamics can be understood as motions along the fibres of a fibre bundle.