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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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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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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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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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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...
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On Optimal Control Problems for Dynamical Systems in Real Time
This paper is a review of the results on the real-time optimal control problem for linear systems obtained by the Minsk school by mathematical...
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Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically,...
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Dynamical Systems
Dynamical systems are mathematical models concerning variables that change depending on time. In this chapter, we consider a system represented by a...
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Controllability of Prabhakar Fractional Dynamical Systems
In this manuscript, we focus on the investigation of controllability results in various types of Prabhakar fractional dynamical systems (FDSs). We...
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Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy...
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Algebraic Dynamical Systems in Machine Learning
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an...
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Dynamical Systems on Graph Limits and Their Symmetries
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than...
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One-dimensional monotone nonautonomous dynamical systems
This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous (cocycle) dynamical systems. A description of the...
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Sensitivity Analysis of Random Linear Dynamical Models Using System Norms
We consider linear dynamical systems with a single output, where the systems include random parameters to perform an uncertainty quantification....