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On the absolute stability approach to quantized feedback control. (English) Zbl 1205.93133
Summary: 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 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.
MSC:
93D20Asymptotic stability of control systems
93B52Feedback control
93C55Discrete-time control systems