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The quantum Kalman decomposition

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Date

2025

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Abstract

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.

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Keywords

Gramian matrix, Hamiltonian matrices, Orthogonal transformation, Quantum Kalman canonical form, Quantum linear control systems, Skew-symmetric matrices, SVD, Symplectic transformation

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https://dspace-test.anu.edu.au/handle/1885/733738942

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DevOps Pure Testing

Source

Automatica

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Article

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DOI

10.1016/j.automatica.2024.112069

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