Ebook: Mathematical Systems Theory: Proceedings of the International Symposium Udine, Italy, June 16–27, 1975

This volume is the record of lectures delivered at the Conference on Mathematical System Theory during the summer of 1975. The conference was held at the International Centre for Mechanical Sciences in Udine, Italy, and was supported by the Consiglio Nazionale delle Richerche of Italy and the International Centre for Mechanical Sciences. The aim of the conference was to encourage fruitful and active collaboration between researchers working in the diverse areas of system theory. It was also the hope of the organizers that mathematicians participating in the conference might become interested in the purely mathematical problems being raised by systems theory as a result of their participation. The success of the conference is to be measured by the extent to which these aims were fulfilled. Besides the formal programme of lectures recorded in this volume, many informal seminars were held. The cafes of Udine were often the scene of rich and varied discussions of recent developments in the field amongst the participants of the conference. Last but not least, listening to the ideas exposed in the lectures of others in a creative atmosphere was an important activity.

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Content:
Front Matter....Pages N1-X
Decomposition Theorems....Pages 1-13
Algebraic Method for Calculating z-Transform....Pages 15-28
The Formal Laplace Transform for Smooth Linear Systems....Pages 29-47
On Invariants, Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems....Pages 48-60
System Invariants under Feedback and Cascade Control....Pages 61-74
Linear Difference Systems on Partially Ordered Sets....Pages 75-91
Estimation of Optimum Structures and Parameters for Linear Systems....Pages 92-110
Functional Expansions and Higher Order Necessary Conditions in Optimal Control....Pages 111-121
Un Outil Algebrique: Les Series Formelles Non Commutatives....Pages 122-148
A Formal Power Series Approach to Canonical Realization of Bilinear Input-Output Maps....Pages 149-164
High Order Algebraic Conditions for Controllability....Pages 165-171
Semigroup Representations, Bilinear Approximation of Input-Output Maps, and Generalized Inputs....Pages 172-191
Algebraic Structure of Infinite Dimensional Linear Systems in Hilbert Space....Pages 193-203
Representation Theory for Linear Infinite Dimensional Continuous Time Systems....Pages 204-225
L2 Systems Theory: Some Applications....Pages 226-236
Algebraic Ideas in Infinite Dimensional System Theory....Pages 237-251
Finiteness in Infinite-Dimensional Systems Applied to Regulation....Pages 252-265
Exponential stabilization of Functional Differential Equations....Pages 266-275
Codes as Elements in a Group Algebra....Pages 277-283
An Introduction to Algebraic Coding Theory....Pages 284-300
Algebraic Structure and Finite Dimensional Nonlinear Estimation....Pages 301-311
Filtering for Random Finite Group Homomorphic Sequential Systems....Pages 312-321
Categorical Approach to Graphic Systems and Graph Grammars....Pages 323-351
Correctness and Equivalence of Data Types....Pages 352-358
Minimization Concepts of Automata in Pseudoclosed Categories....Pages 359-374
Logical and Algebraical Models of the Networks of Activities....Pages 375-392
General Dynamical Systems: Construction and Realization....Pages 393-408
Back Matter....Pages 409-411

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Content:
Front Matter....Pages N1-X
Decomposition Theorems....Pages 1-13
Algebraic Method for Calculating z-Transform....Pages 15-28
The Formal Laplace Transform for Smooth Linear Systems....Pages 29-47
On Invariants, Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems....Pages 48-60
System Invariants under Feedback and Cascade Control....Pages 61-74
Linear Difference Systems on Partially Ordered Sets....Pages 75-91
Estimation of Optimum Structures and Parameters for Linear Systems....Pages 92-110
Functional Expansions and Higher Order Necessary Conditions in Optimal Control....Pages 111-121
Un Outil Algebrique: Les Series Formelles Non Commutatives....Pages 122-148
A Formal Power Series Approach to Canonical Realization of Bilinear Input-Output Maps....Pages 149-164
High Order Algebraic Conditions for Controllability....Pages 165-171
Semigroup Representations, Bilinear Approximation of Input-Output Maps, and Generalized Inputs....Pages 172-191
Algebraic Structure of Infinite Dimensional Linear Systems in Hilbert Space....Pages 193-203
Representation Theory for Linear Infinite Dimensional Continuous Time Systems....Pages 204-225
L2 Systems Theory: Some Applications....Pages 226-236
Algebraic Ideas in Infinite Dimensional System Theory....Pages 237-251
Finiteness in Infinite-Dimensional Systems Applied to Regulation....Pages 252-265
Exponential stabilization of Functional Differential Equations....Pages 266-275
Codes as Elements in a Group Algebra....Pages 277-283
An Introduction to Algebraic Coding Theory....Pages 284-300
Algebraic Structure and Finite Dimensional Nonlinear Estimation....Pages 301-311
Filtering for Random Finite Group Homomorphic Sequential Systems....Pages 312-321
Categorical Approach to Graphic Systems and Graph Grammars....Pages 323-351
Correctness and Equivalence of Data Types....Pages 352-358
Minimization Concepts of Automata in Pseudoclosed Categories....Pages 359-374
Logical and Algebraical Models of the Networks of Activities....Pages 375-392
General Dynamical Systems: Construction and Realization....Pages 393-408
Back Matter....Pages 409-411
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