In a large category of embedded systems, computing resources are limited. Consequently, they need to be exploited as efficiently as possible. Recently, many research works have demonstrated that considering jointly the problems of control and scheduling leads to a better control performance, given the same computing resources. In this paper, the problem of the optimal integrated control and non-preemptive off-line scheduling of control tasks in the sense of the H 2 performance criterion is addressed. It is shown that this problem can be decomposed into two sub-problems which can be solved separately. The first sub-problem aims at finding the optimal non-preemptive off-line schedule, and is solved using efficient Branch and Bound algorithms. The second sub-problem uses the lifting technique to determine the optimal control gains, based on the solution of the first sub-problem. Finally, in order to improve the control performance by dynamically allocating the computational resources, an efficient on-line scheduling heuristic is proposed.M-M. Ben Gaid and A. Ç ela are with the COSI Lab., Y. Hamam is with the A 2 SI Lab., ESIEE, Cité Descartes, BP 99, 93162 Noisy-Le-Grand Cedex, FRANCE and also withConsequently, at instant k l , the relation J rpp (x(0), 0, k l−1 ) + J ss (x rpp (k l ), k l , +∞, p(l)) ≤ J ss (x(0), 0, +∞, p 0 ) holds. When l → +∞, the last relation reduces to J rpp (x(0), 0, +∞) ≤ J ss (x(0), 0, +∞, p 0 )
