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This paper proposes an alternative route to the matrix root clustering problem, which enables to use a result on the common Lyapunov function for solving the problem efficiently. A necessary and sufficient condition is obtained in terms of the existence of a common positive definite solution to a set of Lyapunov inequalities for eigenvalues of a matrix to lie in a prescribed subregion of the complex...
We show in this paper that certain types of polytope of polynomials have parameter-dependent Lyapunov functions. The functions are quadratic ones with coefficients being just the Hermite matrix whose positive definiteness ensures Hurwitz stability of polynomials. It is demonstrated that the polytopes of polynomials have corresponding polytopes of Lyapunov functions and that thereby stability of...
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