Quantized stabilization of continuous-time switched linear systems

Berger, Guillaume;Jungers, Raphaël
(2021) IEEE Control Systems Letters — Vol. 5, n° 1, p. 319-324 (2021)

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Abstract
In this letter, we study the problem of stabilizing continuous-time switched linear systems via mode-dependent quantized state feedback. We derive a closed-form expression for the minimal information data rate from the coder to the controller necessary to achieve stabilization of the system. In particular, it is shown that the evaluation of the minimal data rate for stabilization reduces to the computation of the Lyapunov exponent of some lifted switched linear system, obtained from the original one by using tools from multilinear algebra, and thus can benefit from well-established algorithms for the computation of the Lyapunov exponent. In a second time, drawing upon this expression, we describe a practical coder--controller that stabilizes the system, and whose data rate can be as close as desired to the optimal data rate.
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Berger, G., & Jungers, R. (2021). Quantized stabilization of continuous-time switched linear systems. IEEE Control Systems Letters, 5(1), 319-324. https://doi.org/10.1109/LCSYS.2020.3002068 (Original work published 2021)