Control under quantization, saturation and delay: An LMI approach

• Published in: Automatica (Oxford) 2009-10, Vol.45 (10), p.2258-2264
• Main Authors: Fridman, Emilia, Dambrine, Michel
• Format: Article
• Language: English
• Subjects: Automation; Control systems; Counters; Delay; Inequalities; Linear systems; LMI; Lyapunov–Krasovskii functional; Quantization; Saturation; Time-delay
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.05.020

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 [Fridman, E., Dambrine, M., & Yeganefar, N. (2008). On input-to-state stability of systems with time-delay: A matrix inequalities approach. Automatica, 44, 2364–2369] is extended to the case of saturated quantizer and of quantized state and is based on the simplified and improved Lyapunov–Krasovskii technique.