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Introduction.There is wide range of systems describable as linear Multi Input Multi Variable systems evolving in discrete time. This mathematical model is often used in engineering, but it can also be applied in many other fields. The problem of stabilization of this kind of system frequently arises. In this paper we consider the Model Predictive Control approach to this problem. Its main principle is to generate control signals by optimizing consequent system's future dynamics on limited prediction horizon. While it demonstrates some good results, in practice we are always limited in terms of computational resources. Thus, we can optimize outcomes of our future control sequence only for limited horizon lengths. That is why it is valuable to understand how this limit affects control quality.The purpose of the paper is to propose a way to appraise drawbacks of limiting of the prediction horizon to certain length for a particular system, so that we can make informed choice of such limit and therefore choose controller's microprocessor with sufficient computing power.Methods. Several indexes which characterize the stabilization process are defined. Their heatmaps built against system's initial state are used as a convenient visualization of how system's stabilization dynamics changes depending on its initial state and of drawbacks induced by prediction 39