**Abstract**

Randomized and deterministic algorithms for the problem of LQR optimal control via static-output-feedback (SOF) for discrete-time systems are suggested in this chapter. The randomized algorithm is based on a recently introduced randomized optimization method named the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The randomized algorithm presented here has a proof of convergence in probability to the global optimum. The suggested deterministic algorithm is based on the gradient method and thus can be proved to converge to local optimum only. A comparison between the algorithms is provided as well as the performance of the hybrid algorithm.

**Keywords:** control systems, optimal control, discrete-time systems, state-space models, NP-hard control problems, randomized algorithms, deterministic algorithms
