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Complex Conjugate Matrix Equations for Systems and Control [electronic resource] / by Ai-Guo Wu, Ying Zhang.

By: Wu, Ai-Guo [author.].
Contributor(s): Zhang, Ying [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Communications and Control Engineering: Publisher: Singapore : Springer Nature Singapore : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XVIII, 487 p. 13 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9789811006371.Subject(s): System theory | Control theory | Engineering mathematics | Engineering—Data processing | Algebras, Linear | Control engineering | Systems Theory, Control | Mathematical and Computational Engineering Applications | Linear Algebra | Control and Systems TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 003 Online resources: Click here to access online
Contents:
Introduction -- Mathematical Prelimilaries -- Iterative Approaches -- Finite Iterative Approaches -- Real Representations Based Approaches.-Polynomial Matrices Based Approaches -- Standard Linear Equations Based Approaches -- Conjugate Products -- Con-Sylvester Sums Based Approaches.
In: Springer Nature eBookSummary: The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity.  In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation.
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Introduction -- Mathematical Prelimilaries -- Iterative Approaches -- Finite Iterative Approaches -- Real Representations Based Approaches.-Polynomial Matrices Based Approaches -- Standard Linear Equations Based Approaches -- Conjugate Products -- Con-Sylvester Sums Based Approaches.

The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity.  In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation.

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