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Zbl 1179.93089
Fridman, Emilia; Dambrine, Michel
Control under quantization, saturation and delay: an LMI approach. (English)
[J] Automatica 45, No. 10, 2258-2264 (2009). ISSN 0005-1098

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 $\Bbb R^n$ 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 [{\it E. Fridman, M. Dambrine} and {\it 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 2000:: *93B52 Feedback control
93C15 Control systems governed by ODE
93C05 Linear control systems

Keywords: quantization; time-delay; Lyapunov-Krasovskii functional; LMI; saturation

Citations: Zbl 1153.93502

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