On $l_2$ Stabilization of Linear Systems With Quantized Control

Abstract

This paper extends results from [D. Liberzon and D. Nesic, ldquoInput-to-state stabilization of linear systems with quantized feedback,rdquo IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767--781, May 2007], where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that, by using the same scheme and under the same conditions as in D. Liberzon and D. Nesic, ldquoInput-to-state stabilization of linear systems with quantized feedback,rdquo IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767-781, May 2007, it is also possible to achieve (nonlinear gain) l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stabilization for linear systems. We also prove a new lemma on K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> functions that is interesting in its own right.