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.