Modified Sturm Sequence Property for Damped Systems

This technical note presents a method of checking the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues for nonproportionally damped system. A Schur-Cohn matrix is constructed from the coefficients of the characteristic polynomial for the damped system, and LDLT factorized using some standard numerical algorithms. By observing signs of the diagonal elements of the above diagonal matrix D, we can determine the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues, which is very similar to the well-known Sturm sequence property for undamped systems. To verify the applicability of the proposed method, two numerical examples are considered.