Live briefing
Everything about Linear system
Physical system satisfying the superposition principle
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear systemA 5-minute orientation
- Skim a recent paper: Command Filter-Based Adaptive Fuzzy Finite-Time Output Feedback Control of Nonlinear Electrohydraulic Servo SystemInfluential work since 2022
- Pick up a classic book: Optimization in Engineering SciencesThe most-reprinted book on the subject
- Read the landmark paper: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear SystemsCited 9,151 times
- Go sideways: Linear time-invariant systemA closely related topic
- Go sideways: Superposition principleA closely related topic
📖 Definitions
Noun A mathematical model of a system based on the use of a linear operator.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
General expression of the linear potential sweep voltammogram in the case of diffusionless electrochemical systems
Methods of conjugate gradients for solving linear systems
Preconditioned Quantum Linear System Algorithm
Linear-System Integral Transform Relations
A parallel linear system solver
Linear and Branching System Metrics
ALISS: Advanced Linear Scheduling System
🆕 Influential since 2022
Command Filter-Based Adaptive Fuzzy Finite-Time Output Feedback Control of Nonlinear Electrohydraulic Servo System
QUBO formulations for a system of linear equations
Efficient Use of Quantum Linear System Algorithms in Inexact Infeasible IPMs for Linear Optimization
Short-term system imbalance forecast using linear and non-linear methods
SLE3S-water system: a linear rheological characterisation
📚 Books worth reading
Optimization in Engineering SciencesPierre Borne, Abdelkader El Kamel · 2012
Civil and environmental systems engineeringCharles ReVelle, Charles S. Revelle · 1996
Network analysisM. E. Van Valkenburg · 1955
Signals and linear systemsRobert A. Gabel · 1970
Linear system theory and designChi-Tsong Chen · 1984- 📕Linear Systems and ControlMartin J. Corless, Arthur Frazho · 2003
Signals and systemsSimon S. Haykin, Simon Haykin · 1998
Signal Processing and Linear SystemsB. P. Lathi · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Linear time-invariant system In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal…
- Superposition principle The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli…
- Analog signal processing Analog signal processing is a type of signal processing conducted on continuous analog signals by some analog means (as opposed to the discrete digital…
- Transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function…
- Linear filter Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters…
- Rise time In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified…
- Group delay and phase delay In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal's various sinusoidal…
- State-transition matrix In control theory and dynamical systems theory, the state-transition matrix is a matrix function that describes how the state of a linear system changes…