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In this paper, the static output feedback stabilization for large-scale unstable second-order singular systems is investigated. First, the upper bound of all unstable eigenvalues of second-order singular systems is derived. Then, by using the argument principle, a computable stability criterion is proposed to check the stability of second-order singular systems. Furthermore, by applying model reduction methods to original systems, a static output feedback design algorithm for stabilizing second-order singular systems is presented. A simulation example is provided to illustrate the effectiveness of the design algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the stability of matrix polynomials is investigated. First, upper and lower bounds are derived for the eigenvalues of a matrix polynomial. The bounds are based on the spectral radius and the norms of the related matrices, respectively. Then, by means of the argument principle, stability criteria are presented which are necessary and sufficient conditions for the stability of matrix polynomials. Furthermore, a numerical algorithm is provided for checking the stability of matrix polynomials. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]