Large Language Model (LLM)-powered chatbot agents have proven to be immensely useful in tasks, such as writing and generating essays, code, and academic text. By using frameworks such as LangChain, agents can be equipped with tools to access and analyse custom data, which facilitates bespoke applications, such as customer service agents with access to internal documents and tailored reasoning. While the focus of such applications has mainly centered around textual content, custom toolboxes could also enable agents to act in completely different use cases, for instance control theory. Nevertheless, given the non-deterministic nature of LLMs, merging them with deterministic software implies challenges in applied contexts such as privacy, multi-user interactions, and consistency. To pave the way to reliable LLM usage in various contexts, this work provides the foundation for expanding the use of LLM agents to the domain of control systems and human-centric automation. An agent-based architecture is proposed, which is then implemented within the context of a shared space heating system controlled by three personas. Finally, we evaluate the capacity of the system to deal with scenarios such as normality, erratic user behavior, conflicts of interest, and system limitations. The findings of this study highlight the potential benefits and challenges of using LLMs for appliance control. All code is made public at https://github.com/fredmontet/llm-cps-ac to facilitate further research.