Simultaneous compensation of input delay and state/input quantization for linear systems via switched predictor feedback
Résumé
We develop a switched predictor-feedback law, which achieves global asymptotic
stabilization of linear systems with input delay and with the plant and actuator states
available only in (almost) quantized form. The control design relies on a quantized
version of the nominal predictor-feedback law for linear systems, in which quantized
measurements of the plant and actuator states enter the predictor state formula. A
switching strategy is constructed to dynamically adjust the tunable parameter of the
quantizer (in a piecewise constant manner), in order to initially increase the range and
subsequently decrease the error of the quantizers. The key element in the proof of
global asymptotic stability in the supremum norm of the actuator state is derivation of
solutions' estimates combining a backstepping transformation with small-gain and
input-to-state stability arguments, for addressing the error due to quantization. We
extend this result to the input quantization case and illustrate our theory with a
numerical example.
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