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<p>This paper investigates time-invariant linear quantum state-space (L<i>q</i>SS) systems from an analytical perspective. We establish the existence and uniqueness of solutions by deriving an explicit closed-form representation of this system. Based on this formulation, we characterize the controllability and observability properties of the L<i>q</i>SS system and identify necessary and sufficient conditions that extend the classical state-space theory to the <i>q</i>-calculus setting. In particular, we show that controllability play essential roles in the structural well-posedness of the system, with controllability being closely related to the existence and uniqueness of solutions. An application is presented to illustrate the theoretical findings and to demonstrate the advantages of the proposed analysis.</p>

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Controllability and observability of linear q-state space systems

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Dzaky Muhammad,
  • Kistosil Fahim,
  • Mahmud Yunus,
  • Sunarsini Sunarsini

摘要

This paper investigates time-invariant linear quantum state-space (LqSS) systems from an analytical perspective. We establish the existence and uniqueness of solutions by deriving an explicit closed-form representation of this system. Based on this formulation, we characterize the controllability and observability properties of the LqSS system and identify necessary and sufficient conditions that extend the classical state-space theory to the q-calculus setting. In particular, we show that controllability play essential roles in the structural well-posedness of the system, with controllability being closely related to the existence and uniqueness of solutions. An application is presented to illustrate the theoretical findings and to demonstrate the advantages of the proposed analysis.