On the Observability and Controllability of Linear Fractional Quantum Control Systems

ABSTRACT This paper delves into the analysis of observability and controllability within the framework of time‐invariant linear fractional quantum control systems (LFqCS). Specifically, we explore the ‐Gramian observability matrix of the LFqCS, investigating its rank criteria, null space, and various conditions. Additionally, we discuss the properties of the fractional quantum exponential matrix. We establish that controllability is equivalent to having a controllability matrix with full rank and provide theorems concerning the observability of an LFqCS. Finally, we offer two applications to illustrate the efficacy of our findings.