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L2 stability for quantized linear systems with saturations

Abstract This paper deals with ultimate bounded stability analysis and stabilization conditions for systems involving input saturation and quantized control law, which corresponds to the state quantization case. The state feedback control design problem is then addressed. Theoretical results to ensure the ultimate boundedness and the L 2 stability of the closed-loop system are presented both in local as well as global contexts. The saturation and quantized nonlinearities are tackled through the use of some modified sector conditions. The proposed conditions are then cast in convex optimization problems aiming at maximizing the region of attraction of the closed-loop system and minimizing the set in which the closed-loop trajectories are ultimately bounded, maximizing the bound of admissible L 2 disturbances or maximizing the L 2 -gain from the disturbance to the regulated output.