Quantization error and design of digital control systems

The evolution of the error caused by the amplitude quantization in digital control systems can be studied by introducing bounded disturbances at the points of the quantization. Such a formulation provides an upper bound for the actual quantization error. This paper introduces the problem of the quantization error in the light of the discrete-time optimum control theory. The determination of the worst possible effect of the error due to quantization is reduced to solving a common optimum control problem; the "worst effect" is defined as the maximum of a chosen performance criterion. For a design, a method is proposed for the minimization of the worst effect of the quantization error. Computational solutions illustrate the presentation.