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Stability of a matrix polynomial in continuous systems

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1 Author(s)
Ahn, S. ; General Dynamics, San Diego, CA, USA

Two sufficient conditions under which the roots of the determinant of a given ( m \times m ) matrix polynomial of n th order lie in the open left-half plane have been obtained. The first condition is given in terms of the positive definiteness of an ( mn \times mn ) symmetric matrix, while the second condition is given in terms of the positive definiteness of an ( m \times m ) matrix that is a function of s , Re s \leq 0 . These conditions are represented in terms of rational functions of the coefficient matrices of the given matrix polynomial. Therefore, the explicit computation of the determinant polynomial is not required.

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Automatic Control, IEEE Transactions on  (Volume:28 ,  Issue: 7 )