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In previous work, the authors showed that the dynamics of human blood clotting could be fruitfully modelled and simulated as a hybrid system (HS), that is, one with interacting continuous and discrete parts. Here, the authors show that, although a complete analysis of the HS is (computationally) infeasible, analysis and control techniques can indeed be applied to a large, critical subsystem a set of about 100 ordinary differential equations. The theory is outlined behind the control techniques and then demonstrate in a series of simulations their application to control of pathological blood clotting, both hypercoagulatory (factor-V Leiden) and hypocoagulatory (hæmophilia A). In particular, steering is simulated during a clotting event of the crucial bloodæprotein thrombin, via the controlled injection of (recombinant) factor VIII (for hæmophilia) or the anti-coagulant heparin (for FV Leiden). It remains to remedy the shortcomings of this control technique, and to extend it to the remainder of the HS of the previous work; methods for these are proposed, and addressed in a subsequent article.