Current analysis of functional connectivity networks underlying cognitive states primarily focuses on single-state paradigms within individuals. This limitation affects its applicability to complex unmanned systems operations where operators experience diverse and concurrent multi-category cognitive demands (e.g., workload, attention). This study addresses the unexplored challenge of cross-subject functional connectivity analysis for multi-category cognitive states. We propose a framework utilizing Electroencephalogram (EEG) signal from operators performing tasks with systematically varied cognitive demands. The constructed functional connectivity networks exhibit robust, generalizable neural signatures, notably a shift from segregated to integrated topology with rising cognitive load. A Long Short-Term Memory (LSTM) network validated these signatures by classifying the cognitive states with a mean accuracy of \(87.6\%\) . This identifies robust, generalizable neural signatures and potential neurophysiological biomarkers associated with distinct cognitive demands. Outcomes contribute to developing adaptive human-unmanned system interfaces for enhanced operational efficiency and safety through cross-subject cognitive state assessment.