Citation
Portal Ruiz, Alberto and Zufiria Zatarain, Pedro José
(2019).
On the minimum number of general or dedicated controllers required for system controllability.
"Applied Mathematics and Computation", v. 355
;
pp. 417-427.
ISSN 0096-3003.
https://doi.org/10.1016/j.amc.2019.03.015.
Abstract
The paper determines the minimum number of general or dedicated controllers which are required to guarantee the controllability of a class of dynamical systems. For this purpose, we begin by reformulating Kalman controllability condition for linear systems ( A , B ) in the context of the similarity equivalence class associated with A , and then we provide new al- ternative characterizations of such controllability condition based on the cases when ma- trix A is in Jordan or Frobenius form, so that theoretical aspects and computational re- quirements are comparatively commented. In the second part of the paper, given a system state matrix A , we solve the optimal design problem of determining the minimum number of controllers (columns of B ) required for making ( A , B ) controllable, resorting also to the Jordan and Frobenius canonical forms in the similarity equivalence class associated with A . These canonical forms are proven to be also fundamental to provide bounds on the minimum number of dedicated controllers (corresponding to columns of B with a single non-zero element) required to make ( A , B ) controllable. Some examples serve to illustrate the fundamental results.