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An eight-compartment model of the energy dynamics of an alpine meadow-sheep grazing ecosystem was proposed based on SHIYOMIs system approach. The compartments were the above-ground plant portion, the underground live portion including roots, the underground dead portion including roots, the above-ground litter Ⅰ (degradable portion), the above-ground litter Ⅱ (undegradable portion), the sheep intake, the sheep liveweight, and the faeces. Energy flows between the eight compartments were described by eight simultaneous differential equations. All parameters in the model were determined from paddock experiments.The model was designed to provide a practical method for estimating the effects of the number of rotational grazing subplots, grazing period, and grazing pressure on the performance of grazing systems for perennial alpine meadow pasture. The model provides at least 28 different attributes for characterizing the performance of the grazing system. Analyses of 270 simulated rotational grazing systems of summer-autumn meadow pasture (grazing from 1st June to 30 October each year) provided an inference base to support two recommendations concerning management variables. First, with a three-paddock, 29-day grazing period and 30.14kJ·m-2·day-1 grazing pressure scheme, the system has the highest total grazing intake, 4250.44 kJ·m-2, during the grazing season. Secondly, with a three-paddock, 7-day grazing period and 28.89kJ·m-2·day-1 grazing pressure scheme, the accumulated graze is 4073.34kJ*m-2.The potential productivity of the alpine meadow under grazing is defined in this paper as the maximal dry biomass of herbage grazed by the grazing animals over the whole growing season. It has been analysed by applying optimal control theory to the model. The productivity is regarded as the objective function to be maximized through optimization of the time course of the grazing pressure, the control variable. The results show that: (1) under constant grazing pressure, the optimal grazing pressure is f16=25.90kJ·m-2·day-1 (f46=f56=0) with the highest accumulated intake of J(1)=3268.17kJ·m-2; and (2) the optimal grazing pressure is f16=25.94kJ·m-2·day-1 (f46≠0, f56≠0) with the maxial accumulated intake J(145)=3500.39kJ·m-2. Under variable grazing pressure, the dynamics of optimal grazing pressure is shown in Fig.6(a) and Eqs. (9)(11), while the potential productivity (the highest accumulated intake) is J(145)=8749.01kJ·m-2, 2.5 times the constant grazing pressure.