Upper bounds for the solution norms of the Hermitian ODAE systems

New reachable bounds for the solution norms of the Hermitian systems of ordinary differential and algebraic equations (ODAEs) are proposed and justified. Matrices possessing properties similar to those of pseudo-inverse ones are defined based on the Cauchy integral theorem. These matrices are used to obtain systems of ODEs corresponding to the finite eigenvalues of the original systems. We show that the proposed upper bounds can be computed with known numerical algorithms and compare them with ones based on the Lyapunov equations.