Is More Always Better? Fundamental Trade-Offs Between Information Richness and Dynamic Stability for Heterogeneous Multimodal Communication in 6G Distributed Systems

In distributed wireless systems enabled by multimodal sensing and semantic communication, heterogeneous modalities provide richer task-relevant information but simultaneously introduce asynchronous updates due to modality-dependent sensing, processing, and transmission delays. How such asynchronous multimodal communication affects the dynamic stability of the overall system remains insufficiently understood. This paper investigates the fundamental relationship between semantic information richness and system stability in distributed multimodal wireless communication. To this end, a unified system model is developed in which multimodal semantic streams are embedded into the continuous-time task state evolution, explicitly accounting for heterogeneous delays and MIMO transmission effects. The resulting system is formulated as a delay-coupled dynamic model, and Lyapunov–Krasovskii analysis is employed to characterize the stability conditions under asynchronous semantic updates. An explicit stability perturbation metric is derived to quantify how delayed multimodal information influences system dynamics. The analysis reveals a fundamental trade-off between semantic information richness and dynamic stability: incorporating additional modalities does not always improve system performance and may destabilize the system when asynchronous delays accumulate. Based on this insight, a stability-aware optimization framework is proposed to regulate modality participation and precoding design. The results highlight the necessity of stability-driven multimodal communication design for future distributed wireless and 6G intelligent systems.