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Everything about Exponential stability
Continuous-time linear system with only negative real parts
In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues with strictly negative real parts. A discrete-time input-to-output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. Systems that are not LTI are exponentially stable if their convergence is bounded by exponential decay. Exponential stability is a form of asymptotic stability, valid for more general dynamical systems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Exponential stabilityA 5-minute orientation
- Skim a recent paper: Exponential Stability With RISE ControllersInfluential work since 2022
- Pick up a classic book: Hamiltonian dynamics theory and applicationsThe most-reprinted book on the subject
- Read the landmark paper: Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-lineCited 177 times
- Go sideways: Marginal stabilityA closely related topic
- Go sideways: Linear time-invariant systemA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
Exponential stability in thermoelasticity with microtemperatures
Stability of binary exponential backoff
Exponential stability in linear viscoelasticity
Stability and exponential stability in linear viscoelasticity
Estimate of exponential convergence rate and exponential stability for neural networks
Exponential stability for nonlinear filtering
Exponential stability of uncertain differential equation
🆕 Influential since 2022
Exponential Stability With RISE Controllers
Incremental Versus Differential Approaches to Exponential Stability and Passivity
Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems
Hyers–Ulam Stability, Exponential Stability, and Relative Controllability of Non‐Singular Delay Difference Equations
Sub-exponential stability for the beam equation
📚 Books worth reading
Hamiltonian dynamics theory and applicationsC.I.M.E. - E.M.S. Summer School on Hamiltonian Dynamics Theory and Applications (1999 Cetraro, Italy), Giancarlo Benettin · 2005- 📕Exponentially stable approximations of weakly damped wave equationsH. Thomas Banks · 1991
Differentiable dynamical systemsLan Wen · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- 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…
- BIBO stability In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take…
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- 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…
- Zero-order hold The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That…