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Control under quantization, saturation and delay: an LMI approach. (English) Zbl 1179.93089
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 ${ℝ}^{n}$ 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.
##### MSC:
 93B52 Feedback control 93C15 Control systems governed by ODE 93C05 Linear control systems