Summary: This paper studies quantized and delayed state-feedback control of linear systems with given constant bounds on the quantization error and on the time-varying delay. The quantizer is supposed to be saturated. We consider two types of quantizations: quantized control input and quantized state. The controller is designed with the following property: all the states of the closed-loop system starting from a neighborhood of the origin exponentially converge to some bounded region (both, in
and in some infinite-dimensional state space). Under suitable conditions the attractive region is inside the initial one. We propose decomposition of the quantization into a sum of a saturation and of a uniformly bounded (by the quantization error bound) disturbance. A Linear Matrix Inequalities (LMIs) approach via Lyapunov-Krasovskii method originating in the earlier work [E. Fridman, M. Dambrine
and N. Yeganefar
, Automatica 44, No. 9, 2364–2369 (2008; Zbl 1153.93502
)] is extended to the case of saturated quantizer and of quantized state and is based on the simplified and improved Lyapunov-Krasovskii technique.