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Polynomial and Rational Matrices [electronic resource] :Applications in Dynamical Systems Theory / by Tadeusz Kaczorek.

by Kaczorek, Tadeusz [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Communications and Control Engineering: Publisher: London : Springer London, 2007.Description: XVI, 503 p. online resource.ISBN: 9781846286056.Subject(s): Engineering | Matrix theory | Systems theory | Vibration | Systems engineering | Engineering | Control Engineering | Systems Theory, Control | Vibration, Dynamical Systems, Control | Circuits and Systems | Linear and Multilinear Algebras, Matrix Theory | Electronic and Computer EngineeringOnline resources: Click here to access online
Contents:
Polynomial Matrices -- Rational Functions and Matrices -- Normal Matrices and Systems -- The Problem of Realization -- Singular and Cyclic Normal Systems -- Matrix Polynomial Equations, and Rational and Algebraic Matrix Equations -- The Realisation Problem and Perfect Observers of Singular Systems -- Positive Linear Systems with Delays.
In: Springer eBooksSummary: Matrices are effective tools for the modelling and analysis of dynamical systems. Professor Kaczorek gives an overview of new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. The book is self-contained, beginning with important basics such as the Cayley–Hamilton theorem and definitions and elementary operations of polynomial and rational matrices and moving on to cover such topics as: • normal matrices (including their realisation); • rational and algebraic polynomial matrix equations; • perfect observers for and realisation of linear systems; and • new results on positive linear discrete- and continuous-time systems with delays. The text is rounded off with an appendix describing fundamental definitions and theorems relevant to controllability and observability in linear systems. Polynomial and Rational Matrices will be valuable to researchers in control and/or system theory and will provide useful reference material for graduates studying courses in electronic and computer engineering, mechatronics and electrical engineering.
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Polynomial Matrices -- Rational Functions and Matrices -- Normal Matrices and Systems -- The Problem of Realization -- Singular and Cyclic Normal Systems -- Matrix Polynomial Equations, and Rational and Algebraic Matrix Equations -- The Realisation Problem and Perfect Observers of Singular Systems -- Positive Linear Systems with Delays.

Matrices are effective tools for the modelling and analysis of dynamical systems. Professor Kaczorek gives an overview of new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. The book is self-contained, beginning with important basics such as the Cayley–Hamilton theorem and definitions and elementary operations of polynomial and rational matrices and moving on to cover such topics as: • normal matrices (including their realisation); • rational and algebraic polynomial matrix equations; • perfect observers for and realisation of linear systems; and • new results on positive linear discrete- and continuous-time systems with delays. The text is rounded off with an appendix describing fundamental definitions and theorems relevant to controllability and observability in linear systems. Polynomial and Rational Matrices will be valuable to researchers in control and/or system theory and will provide useful reference material for graduates studying courses in electronic and computer engineering, mechatronics and electrical engineering.

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