Paradigms and puzzles in the theory of dynamical systems
From MaRDI portal
Publication:3981728
DOI10.1109/9.73561zbMath0737.93004OpenAlexW2146560209MaRDI QIDQ3981728
Publication date: 26 June 1992
Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1109/9.73561
Related Items
On higher order linear systems: reachability and feedback invariants ⋮ Topological considerations for autoregressive systems with fixed Kronecker indices ⋮ Dipolynomial minimal bases and linear systems in AR representation ⋮ Kernel representation and properties of discrete-time input-output systems ⋮ Minimality and observability of group systems ⋮ Continuity of singular perturbations in the graph topology ⋮ A cell structure for the set of autoregressive systems ⋮ A behavioral approach to balanced representations of dynamical systems ⋮ A new approach to modeling for control ⋮ An algebraic interpretation of the Laplace transform and of transfer matrices ⋮ Symmetries of differential behaviors and finite group actions on free modules over a polynomial ring ⋮ On generic stabilizability and pole assignability ⋮ Linear dynamical system: compactness theorem ⋮ A bilinear differential forms approach to parametric structured state-space modelling ⋮ A counterexample on dynamical systems described by linear difference inequalities ⋮ The consensus problem in the behavioral approach ⋮ Multidimensional behaviors: the state-space paradigm ⋮ The most powerful unfalsified model for data with missing values ⋮ Reprint of ``A bilinear differential forms approach to parametric structured state-space modelling ⋮ Proper representations of (multivariate) linear differential systems ⋮ Converting high order linear PDEs to first order ⋮ Primeness of multivariate polynomial matrices ⋮ The behavioural approach to systems and control ⋮ A controllability test for general first-order representations ⋮ Canonical state representations and Hilbert functions of multidimensional systems ⋮ Unfalsified plant model parameterization from closed-loop experimental data ⋮ Algorithms for the theory of restrictions of scalar \(n\)-D systems to proper subspaces of \(\mathbb {R}^n\) ⋮ On a new differential geometric setting in nonlinear control ⋮ Model matching under external and input-output equivalence ⋮ Homogeneous behaviors ⋮ Optimal Hankel-norm identification of dynamical systems ⋮ First-order representations of delay-differential systems in a behavioural setting ⋮ Shifts on compact and discrete Lie groups: Algebraic-topological invariants and classification problems ⋮ Difference equations, shift operators and systems over Noetherian factorial domains ⋮ Limits of generalized state space systems under proportional and derivative feedback ⋮ Rational representation of behaviors: Interconnectability and stabilizability ⋮ The linear quadratic optimal control problem for linear descriptor systems with variable coefficients ⋮ Smooth/impulsive linear systems: axiomatic description ⋮ On tangential matrix interpolation ⋮ Every storage function is a state function ⋮ Proper elimination of latent variables ⋮ Canonical kernel representations for behaviors over finite Abelian groups ⋮ The Kalman-Yakubovich-Popov Lemma in a behavioural framework ⋮ The subspace Nevanlinna interpolation problem and the most powerful unfalsified model ⋮ Deterministic Kalman filtering in a behavioral framework ⋮ \({\mathcal H}_{\infty}\) optimal interconnections ⋮ A behavioral approach to the \({\mathcal H}_{\infty}\) optimal control problem ⋮ Identification of factor models by behavioural and subspace methods ⋮ Linear-quadratic control and quadratic differential forms for multidimensional behaviors ⋮ Invariance and polynomial design of strategies in the linear-quadratic game ⋮ Kalman-Popov-Yakubovich Lemma and the \(S\)-procedure: a historical essay ⋮ When are linear differentiation-invariant spaces differential? ⋮ On the state of behaviors ⋮ Discussion on: ``Energy-to-peak model reduction for 2-D discrete systems in Fornasini-Marchesini form ⋮ Relative completeness and specifiedness properties of continuous linear dynamical systems ⋮ Computing the regularization of a linear differential-algebraic system ⋮ First order representations of Fliess models ⋮ Rational differential operators and their kernels ⋮ Axiomatic characterization of linear differential systems (and operators) ⋮ Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data ⋮ On homotopy and similarity in linear systems theory ⋮ Behaviors and symbols of rational matrices ⋮ On the computation of \(\pi\)-flat outputs for linear time-varying differential-delay systems ⋮ Kalman-Popov-Yakubovich lemma for ordered fields ⋮ Asynchronous \(l\)-complete approximations ⋮ Almost direct sum decomposition and implementation of 2D behaviors ⋮ Equivalence conditions for behaviors and the Kronecker canonical form ⋮ Stabilization of discrete 2D behaviors by regular partial interconnection ⋮ A permuted factors approach for the linearization of polynomial matrices ⋮ Checking dissipativity of linear behavior systems given in kernel representation ⋮ Duality in the behavioral systems theory ⋮ A pointwise criterion for controller robustness ⋮ Equations on graphs in \(\mathcal H^{\infty}\)-optimal control problems ⋮ Representations of stochastic processes ⋮ A general realization theory for higher-order linear differential equations ⋮ Discussing some examples of linear system interconnections ⋮ Generic eigenvalue assignment by memoryless real output feedback ⋮ Computation of the generalized inverse of a polynomial matrix and applications ⋮ Closed form solution for the equations of motion for constrained linear mechanical systems and generalizations: an algebraic approach ⋮ Data-driven control: a behavioral approach ⋮ Continuity of dynamical systems: The continuous-time case ⋮ A note on finite memory in locally square integrable systems ⋮ A remark on Willems' trajectory characterization of linear controllability ⋮ Autonomous multidimensional systems and their implementation by behavioral control ⋮ On the Takagi interpolation problem ⋮ State and internal variables for linear systems ⋮ The predictable degree property and row reducedness for systems over a finite ring ⋮ How to define the dual of a higher-dimensional linear system ⋮ On some basics of linear systems theory ⋮ Column reduction of polynomial matrices ⋮ System identifiability from finite time series ⋮ Linear systems with locally integrable trajectories ⋮ On state representations of time-varying nonlinear systems ⋮ The pole-zero cancellation problem in adaptive control: A solution for minimum phase systems by approximate models ⋮ Notes on the definition of behavioural controllability ⋮ Impulse free interconnection of dynamical systems ⋮ A matrix Euclidean algorithm induced by state space realization ⋮ Numerical triangle, Fibonacci sequence and ladder networks: Some further results ⋮ Graphs, causality, and stabilizability: Linear, shift-invariant systems on \({\mathcal L}_ 2[0,\infty\)] ⋮ On the minimal number of trajectories determining a multidimensional system ⋮ A discrete-event model of asynchronous quantised systems ⋮ Every discrete 2D autonomous system admits a finite union of parallel lines as a characteristic set ⋮ Algebraic Theory of Linear Systems: A Survey ⋮ Matrix fraction descriptions in convolutional coding ⋮ The PBH test for multidimensional LTID systems ⋮ A geometric approach to nonlinear dissipative balanced reduction. I: Exogenous signals ⋮ Trajectory encoding for systems with irregular observations ⋮ Why do stabilizing controllers stabilize? ⋮ Minimax control for nonstationary linear operator systems ⋮ Smooth/impulsive linear systems: controllability ⋮ Simultaneous state and input reachability for linear time invariant systems ⋮ Canonical forms for polynomial and quadratic differential operators ⋮ The coarsest lattice that determines a discrete multidimensional system ⋮ The generic dimension of a minimal realization of an AR system ⋮ Continuous state representations for AR systems ⋮ Behaviors defined by rational functions ⋮ Characterising solution sets of LTI differential equations ⋮ Impulsive-smooth behavior in multimode systems. I: State-space and polynomial representations ⋮ An input-output representation for implicit linear time-varying systems ⋮ Disturbance decoupling by behavioral feedback for linear differential-algebraic systems ⋮ Impulsive-smooth behavior in multimode systems. II: Minimality and equivalence ⋮ Duality in time-varying linear systems: A module theoretic approach ⋮ Rank-constrained optimization and its applications ⋮ On the relation between reactive synthesis and supervisory control of non-terminating processes ⋮ \(\ell^2\)-stability: the cases of infinite dimensional discrete autonomous systems and 2-D autonomous systems ⋮ A formal theory of matrix primeness ⋮ On characteristic cones of discrete \(n\)D autonomous systems: theory and an algorithm ⋮ An algorithm for constructing a minimal partial realization in the multivariable case ⋮ On the control of finite support behaviors ⋮ A remark on nonlinear accessibility conditions and infinite prolongations. ⋮ Simultaneous stabilization problem in a behavioral framework ⋮ Implementation of behavioral systems ⋮ Computing the average inter-sample time of event-triggered control using quantitative automata ⋮ Modelling and supervisory control of hybrid dynamical systems via fuzzy \(l\)-complete approximation approach ⋮ A note on Ehrenpreis' fundamental principle ⋮ Stabilization of a class of linear delay systems ⋮ Refinements of behavioural abstractions for the supervisory control of hybrid systems ⋮ A subspace approach to linear dynamical systems ⋮ The simulation problem for high order linear differential systems. ⋮ Foundations of network theory ⋮ Time-delay systems: an overview of some recent advances and open problems. ⋮ On controllability of discrete event systems in a behavioral framework ⋮ A robot control architecture supported on contraction theory ⋮ Structured low-rank approximation and its applications ⋮ Dead beat observer synthesis ⋮ The Nullstellensatz for systems of PDE ⋮ Continuous dependence of linear differential systems on polynomial modules ⋮ Compositionality issues in discrete, continuous, and hybrid systems ⋮ On structural behavioural controllability of linear discrete time systems with delays ⋮ Characterization of linear differential systems (in several variables) ⋮ Unfalsified model parametrization based on frequency domain noise information ⋮ Supervisory control of hybrid systems within a behavioural framework ⋮ Observer theory ⋮ Robust input-output stabilization on \(\mathbb Z\) for persistent signals ⋮ Representations and structural properties of periodic systems ⋮ On state representations of nonlinear implicit systems ⋮ Canonical realizations by factorization of constant matrices ⋮ Controller validation ⋮ A note on the controllability of higher-order linear systems. ⋮ Construction of algebraic and difference equations with a prescribed solution space ⋮ On the reduction of high order linear PDEs to first order ⋮ nD methods for 1D parameter-dependent systems ⋮ Unnamed Item ⋮ A characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms ⋮ On invariant zeros of linear systems of PDEs ⋮ Algebraic tools for the study of quaternionic behavioral systems ⋮ A note on continuous behavior homomorphisms ⋮ On the extension of solutions of linear constant-coefficient PDE ⋮ State space approach to behavioral systems theory: the Dirac--Bergmann algorithm ⋮ A behavioral approach to the control of discrete linear repetitive processes ⋮ A note on persistency of excitation ⋮ Strong controllability and extendibility of discrete multidimensional behaviors ⋮ The canonical controllers and regular interconnection ⋮ State representations of ARMA-models ⋮ Linear systems, and ARMA- and Fliess models ⋮ Autonomy, Controllability, and Extension Modules ⋮ Generalized LFT-based representation of parametric uncertain models ⋮ The behavioral approach as a paradigm for modeling interconnected systems ⋮ Unnamed Item ⋮ Identification of noncontrollable systems from impulse response measurements ⋮ Taylor approximations of multidimensional linear differential systems ⋮ Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems ⋮ New system theory and its impact on control theory ⋮ ARMA-models and their equivalences ⋮ On the solution space of discrete time AR-representations over a finite time horizon ⋮ (Generalised) autoregressive models and their trajectories ⋮ The complementary-slackness class of hybrid systems ⋮ Full information and full control in a behavioral setting ⋮ Interconnections and symmetries of linear differential systems ⋮ The equivalence structure of descriptor representations of systems with possibly inconsistent initial conditions ⋮ On the persistency of excitation ⋮ A hierarchical and modular control architecture for sequential behaviours ⋮ Reconstructibility of time-invariant and periodic behavioural systems ⋮ Smooth/impulsive linear systems: interconnections ⋮ A study of behaviors ⋮ On minimal degree simultaneous pole assignment problems ⋮ Rosenbrock models and their homotopy equivalence ⋮ On some special features which are peculiar to discrete time behaviors with trajectories on \({\mathbb Z}_{+}\) ⋮ Key problems in the extension of module-behaviour duality ⋮ The input-output and controllable behavioural structures of a state space representation ⋮ State-Space Realizations of Periodic Convolutional Codes ⋮ A rigorous framework for interactive robot control ⋮ Observability of Linear Differential-Algebraic Systems: A Survey ⋮ Multidimensional behaviours: an algebraic approach to control theory for PDE ⋮ A parametrisation for dissipative behaviours–the matrix case ⋮ Behavioral Systems Theory: A Survey ⋮ Flatness and defect of non-linear systems: introductory theory and examples ⋮ State-space formulas for the computation of the gap ⋮ A Geometric Approach to Convex Processes: From Reachability to Stabilizability ⋮ Stabilizability of Strict Convex Processes with Respect to Arbitrary Stability Domains ⋮ A low‐dimensional realization algorithm for periodic input/output behavioral systems ⋮ KW Models for (Multivariate) Linear Differential Systems ⋮ A Note on Controlled Invariance for Behavioral nD Systems ⋮ Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades ⋮ On the controllability of distributed systems ⋮ Duality for Multidimensional Linear Systems with Homological Dimension $\leq 1$ ⋮ Autonomous subbehaviours and output nulling subspaces ⋮ A polynomial approach to discrete-time non-linear system controllability ⋮ A new notion of equivalence for discrete time AR representations ⋮ The structure of the state representation of shift invariant controllable and observable group codes ⋮ Controllability of Linear Differential-Algebraic Systems—A Survey ⋮ Approximating distributional behaviour of LTI differential systems using Gaussian function and its derivatives ⋮ Fitting controllers to data ⋮ Representability of impulsive input/output behaviors in descriptor form ⋮ Optimal angle reduction -- a behavioral approach to linear system approximation ⋮ On the structure of linear recurrent error-control codes ⋮ Forward, backward, and symmetric solutions of discrete ARMA representations ⋮ On continuity and consistency of \(\ell_{\infty}\) optimal models ⋮ State-space descriptions and observability properties of 2D finite-dimensional autonomous behaviors. ⋮ On behavior homomorphisms and system equivalence ⋮ Discrete-time average positivity and spectral factorization in a behavioral framework. ⋮ Stability criteria for first-order dynamical systems in a behavioral framework. ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unimodular equivalence and similarity for linear systems ⋮ A two-operator approach to robust stabilization of linear systems on ⋮ Robust Stability of Input-Output Systems with Initial Conditions ⋮ On Minimality of Initial Data Required to Uniquely Characterize Every Trajectory in a Discrete $n$-D System ⋮ State‐space realizations of delay‐differential systems ⋮ Unnamed Item ⋮ On the Role of Well-Posedness in Homotopy Methods for the Stability Analysis of Nonlinear Feedback Systems ⋮ (Singular) state models and (singular) LTID systems