Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Abstract

AbstractThis paper focuses on two main aspects. Firstly, we introduce a generalized form of conformable fractional derivatives called ‐conformable fractional derivatives along with their corresponding integrals . We also present several theorems related to these derivatives. Secondly, we investigate the observability, controllability, and stability of a fractional dynamical system known as the ‐conformable fractional dynamical system ( ‐CF‐DS). We establish the connection between controllability, the controllability matrix, and the fractional ‐conformable fractional differential Lyapunov equation ( ‐CF‐DLE). We prove that the ‐CF‐DS is stable if and only if all eigenvalues of the matrix have negative real parts. Moreover, we provide theorems regarding the observability of an ‐CF‐DS. To demonstrate the efficacy of our results, we include illustrative examples.