TY - JOUR
T1 - The quantum Kalman decomposition
T2 - A Gramian matrix approach
AU - Zhang, Guofeng
AU - Li, Jinghao
AU - Dong, Zhiyuan
AU - Petersen, Ian R.
N1 - Publisher Copyright:
© 2024 Elsevier Ltd
PY - 2025/3
Y1 - 2025/3
N2 - The Kalman canonical form for quantum linear systems was derived in Zhang et al. (2018). The purpose of this paper is to present an alternative derivation using a Gramian matrix approach. Controllability and observability Gramian matrices are defined for linear quantum systems, which are used to characterize various subspaces. Based on these characterizations, real orthogonal and block symplectic coordinate transformation matrices are constructed to transform a given quantum linear system to the Kalman canonical form. An example is used to illustrate the main results.
AB - The Kalman canonical form for quantum linear systems was derived in Zhang et al. (2018). The purpose of this paper is to present an alternative derivation using a Gramian matrix approach. Controllability and observability Gramian matrices are defined for linear quantum systems, which are used to characterize various subspaces. Based on these characterizations, real orthogonal and block symplectic coordinate transformation matrices are constructed to transform a given quantum linear system to the Kalman canonical form. An example is used to illustrate the main results.
KW - Gramian matrix
KW - Hamiltonian matrices
KW - Orthogonal transformation
KW - Quantum Kalman canonical form
KW - Quantum linear control systems
KW - Skew-symmetric matrices
KW - SVD
KW - Symplectic transformation
UR - http://www.scopus.com/inward/record.url?scp=85212392882&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2024.112069
DO - 10.1016/j.automatica.2024.112069
M3 - Article
AN - SCOPUS:85212392882
SN - 0005-1098
VL - 173
JO - Automatica
JF - Automatica
M1 - 112069
ER -