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Everything about Linear dynamical system
Type of mathematical system
Linear dynamical systems are dynamical systems whose evolution functions are linear. While dynamical systems, in general, do not have closed-form solutions, linear dynamical systems can be solved exactly, and they have a rich set of mathematical properties. Linear systems can also be used to understand the qualitative behavior of general dynamical systems, by calculating the equilibrium points of the system and approximating it as a linear system around each such point. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear dynamical systemA 5-minute orientation
- Skim a recent paper: Data-Driven Balancing of Linear Dynamical SystemsInfluential work since 2022
- Pick up a classic book: Guidance of nonlinear nonminimum-phase dynamic systemsThe most-reprinted book on the subject
- Read the landmark paper: Cone of non-linear dynamical system and group preserving schemesCited 151 times
- Go sideways: Phase planeA closely related topic
- Go sideways: Eigenvalues and eigenvectorsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Cone of non-linear dynamical system and group preserving schemes
Optimal Transport Over a Linear Dynamical System
The singular pencil of a linear dynamical system†
Non-linear dynamical system theory and primary visual cortical processing
Arithmetic coding as a non-linear dynamical system
Controllability of a fractional linear time-invariant neutral dynamical system
Controlling dynamical behavior of drive-response system through linear augmentation
LSTM-Based Anomaly Detection for Non-Linear Dynamical System
🆕 Influential since 2022
Data-Driven Balancing of Linear Dynamical Systems
Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system
Controllability and observability for fractal linear dynamical systems
Accelerometer time series augmentation through externally driving a non-linear dynamical system
A Bayesian switching linear dynamical system for estimating seizure chronotypes
📚 Books worth reading
- 📕Guidance of nonlinear nonminimum-phase dynamic systemsSantosh Devasia · 1996
Applied optimal controlArthur E. Bryson · 1969
Modern Linear Control DesignPaolo Caravani · 2013
Nonlinear dynamics of chaotic and stochastic systemsV. S. Anishchenko, Vadim S. Anishchenko · 2002
Dynamical SystemsJürgen Jost · 2005
Linear ChaosAlfred Peris Manguillot · 2011
Control of Linear Parameter Varying Systems with ApplicationsJavad Mohammadpour · 2012
Collective dynamics of nonlinear and disordered systemsG. Radons, W. Just · 2005
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Phase plane In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain…
- Eigenvalues and eigenvectors In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by…
- Matrix differential equation A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and…
- Generalized eigenvector In linear algebra, a generalized eigenvector of an n×n matrix A is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary)…
- Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by A=QDQ−𝟣…
- Lyapunov exponent In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the exponential rate of…
- Eigenfunction In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by…
- Initial condition In mathematics and particularly in dynamical systems, an initial condition is the initial value (often at time t=0) of a differential equation, difference…