Brief paper: On the absolute stability approach to quantized feedback control

Authors:
Bin Zhou;Guang-Ren Duan;James Lam
Affiliations:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, PR China;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, PR China;Department of Mechanical Engineering, University of Hong Kong, Hong Kong
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

By exploring some geometric properties of the logarithmic quantizer and using the fact that the logarithmic quantizer is sector bounded and nondecreasing, this paper presents a new approach to the stability analysis of quantized feedback control systems. Our method is based on Tsypkin-type Lyapunov functions that have been widely used in absolute stability analysis problems. The results are expressed in linear matrix inequalities (LMIs) and are valid for both single-input and multiple-input discrete-time linear systems with a logarithmic quantizer. Both theoretical analysis and numerical examples show that the results in this paper are generally less conservative than those in the quadratic framework.