Zero sets of multiparameter functions and stability of multidimensional systems

New theorems, which can be used to find the zero set of a multiparameter rational function of a complex variable where the distinguished boundary of the parameters´ closed domain of definition is composed of piecewise smooth Jordan arcs or curves, are stated and proved. The results are used to derive a new simplified procedure for a multi-dimensional stability test, presented for the continuous-analog case, as well as for the discrete-digital case. Now proofs to Huang´s and Strintzis´ theorems on multidimensional stability are also provided, as an application of the theorems on zero sets.