The coordinated control of networked integrated energy systems (IESs) is complicated by the different response speeds of the electrical, gas, and thermal subsystems and by information exchange over directed communication graphs. Existing studies mainly consider the economic scheduling of a single IES, dynamic modeling of individual systems, or cooperative control of systems with two time scales, and therefore, they do not provide a unified supervisory framework for coordinating three energy domains with an explicit performance bound. This paper investigates whether a common leader-following framework can coordinate the principal variables of the three energy domains while limiting both regulation errors and control effort. Each IES is treated as an agent, the three energy domains are represented by separate reduced dynamic blocks sharing a common directed communication topology, and a distributed state feedback controller is developed using relative information, Riccati-based gain design, and complete Lyapunov analysis. Simulations of a network of four IESs show that the longest settling times in the electrical and gas domains are approximately 0.05 s and 5.41 s, respectively, whereas the thermal disagreement decreases by 96.5% over 300 s; the accumulated cost remains below its calculated upper bound in the nominal case and in all three time-scale settings, while a separate numerical communication reconfiguration case illustrates bounded responses during communication link removal and reconnection. These results demonstrate that the proposed framework can simultaneously coordinate variables with substantially different response speeds while accounting for regulation accuracy and control effort under the stated reduced model and fixed graph assumptions. The communication reconfiguration case provides a numerical illustration and does not constitute a general stability guarantee for arbitrary topology switching.
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