On the robust control design of quantized systems

When implementing a controller in a digital computer or when realizing digital filters, the numerical effects from the quantisation of the state, due to adder overflow, magnitude truncation or finite-wordlength format, may introduce severe nonlinearities. As soon as A/D and D/A conversions get involved, a behavioral study of the quantized system is compulsory to ensure stability of the real system. We propose in this paper a linear matrix inequality approach for the stabilization of uncertain quantized systems.