Robustness of quantized control systems with mismatch between coder/decoder initializations

Abstract

This paper analyzes the stability of linear systems with quantized feedback in the presence of mismatch between the initial conditions at the coder and decoder. Under the assumption of the perfect channel, we show that using the scheme proposed in [Liberzon, D., & Nešić, D. (2007). Input-to-state stabilization of linear systems with quantized state measurements. Institute of Electrical and Electronic Engineers Transaction on Automatic Control, 52, 767–781] it is possible to achieve stability with exponential convergence of linear systems with quantized feedback when the coder and decoder are initialized at different initial conditions.