Output Controllability of Fractional-Order Systems with Generalized Caputo Proportional Operators
Keywords:
Output controllability, Generalized fractional derivative, Kalman rank condition, Controllability Gramian, Nonlinear systemsAbstract
This paper presents a mathematically rigorous contribution to the study of output controllability for fractional-order systems governed by generalized Caputo proportional operators. First, we establish necessary and sufficient conditions for the output controllability of linear time-invariant fractional systems in terms of the fractional output controllability Gramian, and we derive a Kalman-type rank condition that provides a practical criterion for verifying controllability. Then, we extend the analysis to nonlinear fractional systems and establish sufficient conditions for output controllability by applying Schauder’s fixed point theorem. A numerical example is included to illustrate the effectiveness of the proposed results.
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Copyright (c) 2026 Amel Merghad, Salah Eddine Rebiai
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