Application of Hankel matrices of Markov parameters to the solutions of the Routh-Hurwitz and the Schur-Cohn problems

DOI10.1016/0022-247X(79)90115-XzbMath0421.65035MaRDI QIDQ1133292

Biswa Nath Datta

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Markov parametersHankel matricesRouth-Hurwitz and the Schur-Cohn problems

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of solutions to single equations (65H05) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10) Nonlinear algebraic or transcendental equations (65H99)

Related Items (12)

Hurwitz polynomials and orthogonal polynomials generated by Routh-Markov parameters ⋮ Linear matrix equations: The module theoretic approach ⋮ Unnamed Item ⋮ On the parallel arithmetic complexity of the root-finding problem ⋮ Stability and inertia ⋮ A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices ⋮ A Favard type theorem for Hurwitz polynomials ⋮ The Bezoutian and the eigenvalue-separation problem for matrix polynomials ⋮ An analysis and synthesis of the classical Fujiwara methods for the root- separation problems ⋮ Generalized Hankel matrices of Markov parameters and their applications to control problems ⋮ Polynomials and Hankel matrices ⋮ On matrix Hurwitz type polynomials and their interrelations to Stieltjes positive definite sequences and orthogonal matrix polynomials

Cites Work

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• Some theorems on the inertia of general matrices
• Inertia theorems for matrices, controllability, and linear vibrations
• Matrices \(C\) with \(C^ n\to 0\)
• A remark on a theorem of Lyapunov
• Matrix equations and the separation of matrix eigenvalues
• Inertia theorems for matrices: the semidefinite case
• On the Ostrowski-Schneider inertia theorem
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• Application of Hankel matrix to the root location problem
• Application of the Second Method of Lyapunov to the Proof of the Markov Stability Criterion
• Matrices, polynomials, and linear time-variant systems

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