This volume is the first of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathematical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989. The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is typical for MTNS, turns out to be most effective and is, as these proceedings show, a continuing source of exciting advances. The first volume contains invited papers and a large selection of other symposium presentations on the general theory of deterministic and stochastic systems with an emphasis on realization and modelling. A wide variety of recent results on approximate realization and system identification, stochastic dynamical systems, discrete event systems,- o systems, singular systems and nonstandard models IS presented. Preface vi Also a few papers on applications in hydrology and hydraulics are included. The titles of the two other volumes are: Robust Control of Linear Sys tems and Nonlinear Control (volume 2) and Signal Processing. Scatter ing and Operator Theory. and Numerical Methods (volume 3). The Editors are most grateful to the about 300 reviewers for their help in the refereeing process. The Editors thank Ms. G. Bijleveld and Ms.

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Invited Papers.- Questioning the classic state-space description via circuit examples.- Noncausal estimation for discrete Gauss-Markov random fields.- Process models for discrete event systems.- A framework for the study of dynamical systems.- Correspondence of internal and external stability Realization functions and complex analysis.- Transformations and Representations of Systems.- State-space and polynomial approaches to rational interpolation.- The Kähler structure of the total least squares problem, Brockett's steepest descent equations, and constrained flows.- Some canonical properties of nonlinear systems.- Differential algebraic modelling of nonlinear systems.- Transformation issues in linear system theory.- Another look at the Brayton-Moser network equations.- Input/ output equations and realizability.- Balancing general quadratic measures on external signals.- The Topology of Linear Systems.- Lie algebraic generalizations of Hessenberg matrices and the topology of Hessenberg varieties.- The moduli space of controllable singular systems under restricted system equivalence.- A note on the geometry of partial realization.- The numerical stability of observability.- Algebraic Geometry and Linear Systems.- On BC S-rings and the pole shifting problem for linear systems.- Matching via measurement feedback.- Algebraic-geometric techniques for linear periodic discrete-time systems.- Zeros at infinity for infinite dimensional systems.- The pole module of a feedback compensator system is contained in the zero module of the resulting feedback system.- On stabilization and the existence of coprirne factorizations.- Continuous pole shifting for parametric families of systems.- The Riccati fiow near the edge.- Singular Systems.- Reachability and controllabilitysubspaces for singular systems: A matrix pencil characterization.- Classification of subspaces of singular systems: A number theoretic approach.- A classification of minimal bases for singular systems.- Some useful aspects of the infinite structure in singular systems.- On infinite zeros for generalized linear systems.- Non-Standard Models in System Theory.- Multiscale statistical signal processing: Stochastic processes indexed by trees.- Realization theory for deterministic boundary-value descriptor systems.- Two-Dimensional Systems.- An algebraic test for internal stability of 2-D discrete systems.- On some algebraic aspects of 2D dynamic feedback control.- Recursive reconstruction of image from noisy and blurred multiframes.- Computation of the fundamental matrix sequence and the Cay ley-Hamilton theorem in singular 2-D systems.- A state representation for 2-D systems.- Markovian properties for 2-D systems.- 2D transfer functions and stability tests for discrete linear multipass processes.- Bilinear Systems.- Constant feedback stabilizability of bilinear systems.- The parameter sensitivity of bilinear dynamical systems.- Approximate bilinear realizations: an application to diffusion processes.- Approximate Realization.- Interpolation and Fourier coefficients in the Hardy space H2.- Approximation of linear systems under the constraint of steady-state values of the step responses.- Canonical variate modelling and approximation of linear systems.- Experimental analysis of robust solutions to three problems related to the partial realization problem.- System Identification.- Structural identifiability conditions for systems operating in closed loop.- A Imost sure asymptotics of Rissanen's predictive stochastic complexity.- System identifiability for the procedure ofmost powerful unfalsified modeling.- Identification in H-infinity: A robustly convergent nonlinear algorithm.- Identification/prediction algorithms for ARMAX models with relaxed positive real conditions.- An identification procedure for linear continuous time systems with jump parameters.- On discriminable model sets in residual-based system identification.- Stochastic Dynamical Systems and Statistical Physics.- Stochastic differential equations as dynamical systems.- On the Markov processes of Schroedinger, the Feynman-Kac formula and stochastic control.- Hamiltonian models of classical and quantum stochastic processes.- Stochastic aggregation of linear Hamiltonian systems with microcanonical distribution.- A stochastic integral representation for functional of diffusions on manifolds.- Discrete Event Systems.- Reachability of LSFC Nets.- On controllable languages in supervisory control of discrete event systems.- Petri-net-based fairness concepts for discrete event systems.- Discrete event systems and deadlock.- Hydrology and Hydraulics.- Simplified adaptive Kalman filtering for large-scale geophysical models.- The calibration of 2-D shallow water flow models.- Domain decomposition for data assimilation in flow forecasting models.