Abstract: method for determining the stability of dynamic system is discussed in this paper.In the method the coefficient matrix of the differential equations of dynamical system A=(a_ij)n×n is transformed to upper Hessenberg fonn by similarity transformation. Based on the diagonal matrix D=[d_ij] obtained by interative procedures of change parameters,the stability of origi-nal system A is determined.The characteristic equations or eigenvalues of the matrix A need not be calculated by this method,it is convenient to detennine the stability of large scale system.The application of the method is illustrated by an example.

Key words: motion stability, transformation mathematics, matrix theory