Geometric characterization of multivariable quadratically stabilizing quantizers

HERNAN HAIMOVICH; MARÍA M. SERON; GRAHAM C. GOODWIN

INTERNATIONAL JOURNAL OF CONTROL

Taylor & Francis Ltd

Lugar: Oxford, UK; Año: 2006 vol. 79 p. 845 - 857

0020-7179

In this paper, we present an explicit geometric characterization of quadratically stabilizing state feedback laws that are based on the use of multivariable quantizers of minimum dimension. This characterization consists of a set of necessary and sufficient conditions for a quantized static state feedback to render a given quadratic function a Lyapunov function for the closed-loop system. These necessary and sufficient conditions provide a means to analyse and design such quantized feedback laws and are derived from set inclusion conditions that are necessarily satisfied by the quantization regions and values of a quadratically stabilizing quantizer.