On the relationships between the unbounded asymptote behaviour of multivariable root loci, impulse response and infinite zeros

DOI10.1080/00207178108922513zbMath0469.93038OpenAlexW4246974677MaRDI QIDQ3924033

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Publication date: 1981

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207178108922513

zbMATH Keywords

rational matrixlinear multivariable systemssingular-value decompositionorthonormal basesinfinite zerosmultivariable root locusSchur complement for a partitioned matrixSmith-MacMillan zerosvector- impulse inputs

Mathematics Subject Classification ID

Factorization of matrices (15A23) Multivariable systems, multidimensional control systems (93C35) Linear systems in control theory (93C05) Eigenvalues, singular values, and eigenvectors (15A18) Algebraic methods (93B25) Realizations from input-output data (93B15)

Related Items (8)

Multivariate root-locus behaviour and the relationship to transfer-function pole-zero structure† ⋮ Unified theory of impulse transmission, infinite zeros, and the unbounded asymptotic behaviour of MIMO systems ⋮ Simultaneous finite- and infinite-zero assignments of linear systems ⋮ Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling ⋮ A singular perturbation canonical form of invertible systems: determination of multivariate root-loci ⋮ Research on system zeros: a survey ⋮ Singular perturbations and time-scale methods in control theory: Survey 1976-1983 ⋮ Multivariable feedback: a personal reminiscence

Cites Work

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• Properties and calculation of transmission zeros of linear multivariable systems
• A complex variable approach to the analysis of linear multivariable feedback systems
• Comments on ‘ On structural invariants and the root-loci of linear multivariable systems’
• On the zeros and poles of a rational matrix
• Asymptotic behaviour of root-loci of linear multivariable systems
• The generalized Nyquist stability criterion and multivariable root loci
• Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory
• Multivariate root loci: a unified approach to finite and infinite zeros

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