Light emitting diode (LED)-based systems are considered to be the future of lighting. We consider the problem of energy-efficient illumination control of such systems. Energy-efficient system design is based on two aspects: localised information on occupancy and optimisation of dimming levels of the LEDs. Specifically, we are interested in minimising the power consumption of an LED system, subject to providing uniform illumination at a pre-specified level around occupied zones, by determining the dimming levels of the LEDs. We show that this optimisation problem can be solved by linear programming and use the simplex algorithm to determine the dimming levels. The efficacy of our proposed system is evaluated in an office scenario by comparing it with a system that renders uniform illumination across the whole space.