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This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear systems. This monographs summarizes recent original investigations of the authors in the new field of the positive and fractional linear systems.
List of contents
Realization problem of 1D standard linear systems.-
Realization problem of 1D positive regular linear systems.-
Realization problem of 1D positive regular linear systems
with delays.-
Positive stable realization problem for 1D regular linear systems.-
Positive realization problem of 1D descriptor linear systems.-
Positive realization problem for 1D regular fractional
linear systems.-
Positive realization problem for 1D descriptor fractional
linear systems.-
Positive realization problem for 2D continuous-discrete
linear systems.
Summary
This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear systems. This monographs summarizes recent original investigations of the authors in the new field of the positive and fractional linear systems.
Additional text
From the book reviews:
“The problems and facts of interest are presented in a very well organized manner and the usual roughness of some technical aspects is avoided by treating them in a natural way, closer to a practical engineering approach. … The monograph gives a complete presentation of the state of the art in the theory of system realization, and will be a fruitful reading for researchers at all levels in this area.” (Tiberiu Vasilache, Mathematical Reviews, January, 2015)
“The book is well, clearly written and hence is easy to follow for the reader. There are many illustrating examples. The book is recommended for researchers and students who are interested in the modern system theory.” (Krzysztof Gałkowski, zbMATH, Vol. 1297, 2014)
Report
From the book reviews:
"The problems and facts of interest are presented in a very well organized manner and the usual roughness of some technical aspects is avoided by treating them in a natural way, closer to a practical engineering approach. ... The monograph gives a complete presentation of the state of the art in the theory of system realization, and will be a fruitful reading for researchers at all levels in this area." (Tiberiu Vasilache, Mathematical Reviews, January, 2015)
"The book is well, clearly written and hence is easy to follow for the reader. There are many illustrating examples. The book is recommended for researchers and students who are interested in the modern system theory." (Krzysztof Galkowski, zbMATH, Vol. 1297, 2014)
