Geometry of cascade feedback linearizable control systems

Cascade feedback linearization provides geometric insights on explicit integrability of nonlinear control systems with symmetry. A central piece of the theory requires that the partial contact curve reduction of the contact sub-connection be static feedback linearizable. This work establishes new necessary conditions on the equations of Lie type -in the abelian case -that arise in a contact sub-connection with the desired static feedback linearizability property via families of codimension one partial contact curves. Furthermore, an explicit class of contact sub-connections admitting static feedback linearizable contact curve reductions is presented, hinting at a possible classification of all such contact sub-connections. Key tools in proving, and stating, the main results of this paper are truncated versions of the total derivative and Euler operators. Additionally, the Battilotti-Califano system with three inputs is used as a clarifying example of both cascade feedback linearization and the new necessary conditions.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

Cascade feedback linearization provides insights on explicit integrability of nonlinear control systems with symmetry. This work establishes new necessary conditions for the static feedback linearizability property of contact sub-connections, using Lie-type equations in the abelian case and partial contact curves. It also presents an explicit class of contact sub-connections that admit static feedback linearizable contact curve reductions, possibly leading to a classification of all such sub-connections.