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A Note on Quaternion Linear Dynamical Systems
We established conditions of stability and instability of quaternion linear dynamical systems, linear differential and linear fractional equations.
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Data-driven discovery of linear dynamical systems from noisy data
In modern science and engineering disciplines, data-driven discovery methods play a fundamental role in system modeling, as data serve as the...
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Two-Dimensional Linear Dynamical Systems
In this Chapter, two-dimensional dynamical systems with constant and linear vector fields are discussed. Dynamical systems with one-variable vector...
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On Some Constructions of Regular Linear Extensions of Dynamical Systems on a Torus
We study Lyapunov functions in the form of a linear combination of quadratic forms and investigate the regularity conditions for linear extensions of...
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Monotone Linear Dynamical Systems over Dioids
Linear systems over naturally ordered dioids are other kinds of positive systems than the usual ones over semiring (...
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Event-triggered Synchronization for Second-order Linear Systems in Complex Dynamical Network With Time-varying Topology
In this paper, the event-triggered synchronization of second-order linear systems in complex dynamical networks (CDNs) with time-varying topology is...
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Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods
Linear multistep methods (LMMs) are popular time discretization schemes for solving the forward problem on differential equations. Recently, LMMs...
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On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data
Learning controllers from data for stabilizing dynamical systems typically follows a two-step process of first identifying a model and then...
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Data-driven modeling of interrelated dynamical systems
Non-linear dynamical systems describe numerous real-world phenomena, ranging from the weather, to financial markets and disease progression....
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Interpretable predictions of chaotic dynamical systems using dynamical system deep learning
Making accurate predictions of chaotic dynamical systems is an essential but challenging task with many practical applications in various...
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Deep multi-modal learning for joint linear representation of nonlinear dynamical systems
Dynamical systems pervasively seen in most real-life applications are complex and behave by following certain evolution rules or dynamical patterns,...
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Green–Samoilenko Function of Linear Extensions of Dynamical Systems on a Torus
We study criteria for the existence of the Green–Samoilenko function for linear extensions of dynamical systems on a torus. The structures of...
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Continuous Dynamical Systems
DynamicsDynamics is a time-evolutionary process. It may be deterministic or stochastic. Long-term predictions of some systems often become...
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A New Scheme for the Approximation of Linear Dynamical Systems and Its Application to Controller Design
A new hybrid scheme of model order reduction (MOR) technique is developed for the simplification and control design of linear large-scale dynamical...
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Model Checking Linear Dynamical Systems under Floating-point Rounding
We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are...
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Actively learning dynamical systems using Bayesian neural networks
Learning dynamical systems in a sample-efficient way is important for model-based control. Active learning which sequentially selects the most...
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Comparison Theorems from the Theory of Monotone Dynamical Systems for Linear Systems of Functional-Differential Equations with Linearly Transformed Argument
We find new properties of solutions to the linear systems of functional-differential equations with linearly transformed argument.
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition...
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Observability of Time-Varying Fractional Dynamical Systems with Caputo Fractional Derivative
Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative...
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Algorithms for Robust Inversion of Dynamical Systems
AbstractA new methodology for solving inverse dynamics problem is developed. The methodology is based on using a mathematical model of a dynamical...