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The paper considers pseudo-differential boundary value control systems. Theunderlying operators form an algebra D with the help of which we are able toformulate typical boundary value control problems. The symbolic calculus givestools to form e.g. compositions, formal adjoints, generalized right or leftinverses and compatibility conditions. By a parametrizability we mean that fora given control system Au=0 one finds an operator S such that Au=0 if and onlyif u=Sf. The computation rules of D (or its appropriate subalgebra D')guarantee that in many applications S can be refinely analyzed or evenexplicitly calculated. We outline some methods of homological algebra for thestudy of parametrization S. Especially the projectivity of a certain factormodule (defined by the system equations) implies the parametrizability. We givesome examples to illustrate our computational methods.

On parametrization of linear pseudo-differential boundary value control systems