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.

Inhalt

1. Automata Theory.- Decomposition Theorems.- 2. Linear Systems Theory.- Algebraic Method for Calculating z-Transform.- The Formal Laplace Transform for Smooth Linear Systems.- On Invariants, Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems.- System Invariants under Feedback and Cascade Control.- Linear Difference Systems on Partially Ordered Sets.- Estimation of Optimum Structures and Parameters for Linear Systems.- 3. Bi-Linear and Non-Linear Systems.- Functional Expansions and Higher Order Necessary Conditions in Optimal Control.- Un Outil Algebrique: Les Series Formelles non Commutatives.- A Formal Power Series Approach to Canonical Realization of Bilinear Input-Output Maps.- High Order Algebraic Conditions for Controllability.- Semigroup Representations, Bilinear Approximation of Input-Output Maps, and Generalized Inputs.- 4. Infinite Dimensional Systems.- Algebraic Structure of Infinite Dimensional Linear Systems in Hilbert Space.- Representation Theory for Linear Infinite Dimensional Continuous Time Systems.- L2 Systems Theory: Some Applications.- Algebraic Ideas in Infinite Dimensional System Theory.- Finiteness in Infinite-Dimensional Systems Applied to Regulation.- Exponential Stabilization of Functional Differential Equations.- 5. Coding and Filtering for Sequential Systems.- Codes as Elements in a Group Algebra.- An Introduction to Algebraic Coding Theory.- Algebraic Structure and Finite Dimensional Nonlinear Estimation.- Filtering for Random Finite Group Homomorphic Sequential Systems.- 6. General Dynamical Systems and Categorical Approach to Systems.- Categorical Approach to Graphic Systems and Graph Grammars.- Correctness and Equivalence of Data Types.- Minimization Concepts of Automata in Pseudoclosed Categories.- Logical and Algebraical Models of the Networks of Activities.- General Dynamical Systems: Construction and Realization.