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Stability notion for nonlinear control systems with external inputs
Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking
Input-to-state_stability
When a system's outputs are bounded for every bounded input
control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable
BIBO_stability
Property of a dynamical system where solutions near an equilibrium point remain so
to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs. Lyapunov stability is named after Aleksandr Mikhailovich
Lyapunov_stability
Theorem used for studying closed-loop stability
of input-output stability is an important tool in studying the stability of interconnected systems since the gain of a system directly relates to how
Small-gain_theorem
Topics referred to by the same term
(Bounded Input, Bounded Output stability), in signal processing and control theory Directional stability, the tendency for a body moving with respect to a medium
Stability
holds that The comparison-functions formalism is widely used in input-to-state stability theory. E. D. Sontag. Comments on integral variants of ISS. Systems
Comparison_function
Branch of engineering and mathematics
systems. The aim is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing
Control_theory
Chinese-American control theorist
mathematician specializing in control theory and known for her research on input-to-state stability. She is a professor of mathematics at Florida Atlantic University
Yuan_Wang_(control_theorist)
Continuous-time linear system with only negative real parts
proper to state that a system is exponentially stable over a certain range of inputs. Exponentially stable semigroup Marginal stability State space (controls)
Exponential_stability
Argentine American mathematician
Group. His work in control theory led to the introduction of the concept of input-to-state stability (ISS), a stability theory notion for nonlinear systems
Eduardo_D._Sontag
Mathematical model of a system in control engineering
identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior
State-space_representation
Dynamical system which is neither asymptotically stable nor unstable
sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it
Marginal_stability
Uncertain Constrained Nonlinear Systems: Recursive Feasibility and Input-to-State Stability Analysis". IEEE Transactions on Automatic Control. 56 (1): 72–87
Networked_control_system
American control theorist
co-authored with Alexander Scheinker; Springer. ISBN 978-3-319-50790-3 Input-to-State Stability for PDEs (2018), co-authored with Iasson Karafyllis; Springer.
Miroslav_Krstić
Intermediate energetic state within a dynamical system
thermodynamic trough without being at the lowest energy state is known as having kinetic stability or being kinetically persistent. The particular motion
Metastability
Logemann, Hartmut; Ryan, Eugene (2011). "The Circle Criterion and Input-to-State Stability". IEEE Control Systems Magazine. 31 (4): 32–67. doi:10.1109/MCS
Aizerman's_conjecture
Quantitative economic model
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy
Input–output_model
Computerized safety automotive technology
Electronic stability control (ESC), also referred to as electronic stability program (ESP) or dynamic stability control (DSC), is a computerized technology
Electronic_stability_control
In stability theory, hyperstability is a property of a system that requires the state vector to remain bounded if the inputs are restricted to belonging
Hyperstability
Lebanese-Greek-American mathematician
partial stability, Lagrange stability, boundedness, ultimate boundedness, input-to-state stability, input-output stability, finite-time stability, semistability
Wassim_Michael_Haddad
Graphical method of determining the stability of a dynamical system
generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplanes. The Nyquist stability criterion is
Nyquist_stability_criterion
Process where information about current status is used to influence future status
system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself
Feedback
Function specifying the behavior of a component in an electronic or control system
distribution and stability of a reactor. In simple cases, this function can be represented as a two-dimensional graph of an independent scalar input versus the
Transfer_function
Numerical measures that characterize amplifier properties and performance
underdamped circuit. In response to a step input, the overshoot is the amount the output exceeds its final, steady-state value. Stability is an issue in all amplifiers
Amplifier_figures_of_merit
System in which not only one independent variable exists
dimension has a state vector that contains the effect of prior inputs relative to that dimension. The collection of all such dimensional state vectors at a
Multidimensional_system
Function in control theory
For asymptotic stability, the state is also required to converge to x = 0 {\displaystyle x=0} . A control-Lyapunov function is used to test whether a
Control-Lyapunov_function
Number of states of a cybernetic system
distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the
Variety_(cybernetics)
Electronic circuit with two stable states
can store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will
Flip-flop_(electronics)
High-gain voltage amplifier with a differential input
including: Stability Associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead to oscillation
Operational_amplifier
Audio compressor
compressors, it marked the transition from tube to solid-state technology. The limiter featured Class A amplifiers, input and output transformers, fast attack and
1176_Peak_Limiter
Control concept
tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances. Whereas positive feedback tends to instability
Negative_feedback
Higher Studying Field
one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure's geometric representation
Structural_mechanics
System designed to maintain a constant voltage
tends to increase regulation accuracy but reduce stability. Stability is the avoidance of oscillation, or ringing, during step changes in load or input voltage
Voltage_regulator
Type of software test
impractical. It depends not only on the software to be repeatable but also on the stability of the environment and input values. Golden Master testing does not
Characterization_test
approach to ensure stability in cases of large model uncertainty or changing plant dynamics. It uses a number of models, which are distributed to give a
Multiple_models
applications and is relevant to analyzing many fundamental steady-state closed-loop system properties such as stability and robustness. Given a linear
Relative_gain_array
Characteristic polynomial whose associated linear system is stable
time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output. A linear system is BIBO stable
Stable_polynomial
Series of transistor–transistor logic integrated circuits
unsuitable to be used as analog devices, providing low gain, poor stability, and low input impedance. Special-purpose TTL devices were used to provide interface
7400-series integrated circuits
7400-series_integrated_circuits
Ratio of output to input as a function of frequency
shift of the output relative to the input. The frequency sweep must be slow enough for the system to reach its steady-state at each point of interest Applying
Frequency_response
Dependence of the state of a system on its history
exist an input at which the cell jumps to the next stable state, but there is no input that allows the cell to revert to its previous stable state, even
Hysteresis
Electronic control system
relative to the phase of an input signal. Keeping the input and output phase in lockstep also implies a constant relationship between input and output
Phase-locked_loop
Metaphorical term for a process that builds upon itself
returned to its input filtered to contain primarily the selected (desired) frequency, gradually getting stronger in each cycle, until a steady-state oscillation
Snowball_effect
susceptible to significant errors due to bias or leakage currents. Practical operational amplifiers draw a small current from each of their inputs due to bias
Operational amplifier applications
Operational_amplifier_applications
Family of macroeconomic models
models into agent-based modeling (ABM) or input–output models. Current researchers in the SFC approach to macroeconomic modelling are based in University
Stock-flow_consistent_model
Algorithm for supervised learning of binary classifiers
is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier
Perceptron
Machine learning model
networks. In 2022, the output of state-of-the-art text-to-image models—such as OpenAI's DALL-E 2, Google Brain's Imagen, Stability AI's Stable Diffusion, Midjourney
Text-to-image_model
Electronic system for generating any of a range of frequencies
phase-locked loops to generate its frequencies. The stability and accuracy of the frequency synthesizer's output are related to the stability and accuracy of
Frequency_synthesizer
Set of assumptions in macroeconomics
ensure the existence of a unique and stable steady state, and promote smooth substitution between inputs. A Cobb–Douglas production function satisfies the
Inada_conditions
Approach in control theory to achieve fault-tolerant control for dynamic systems
the state trajectory recovery goal, which requires that the state trajectory be restored to the nominal case by the reconfiguration under any input. Usually
Control_reconfiguration
Time behavior of a system controlled by Heaviside step functions
response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic
Step_response
Concept in physiology
on the sensory input to achieve perceptual stability. Together with internal models, efference copies can serve to enable the brain to predict the effects
Efference_copy
Parameter of phase-locked loop engineering
also called steady-state stability. In addition, for a frequency deviation within the hold-in range, after a small changes in input frequency loop re-achieves
Phase-locked_loop_range
Use of digital computers as system controllers
transient response and stability of the compensated system, and must update the values at the controller input often enough so as to not cause instability
Digital_control
the Lyapunov equation in stability theory. It establishes a relation between a linear matrix inequality involving the state space constructs A, B, C and
Kalman–Yakubovich–Popov_lemma
Main European Union fiscal agreement
Stability and Growth Pact (SGP) is an agreement, among all the 27 member states of the European Union (EU), to facilitate and maintain the stability of
Stability_and_Growth_Pact
Values which describe behavior of a linear electric circuit
feedback from the output of an amplifier to the input and therefore influences its stability (its tendency to refrain from oscillation) together with the
Scattering_parameters
Trade restrictions levied by the United States government
sometimes in conjunction with the State, Defense, or Energy departments. Comprehensively sanctioned jurisdictions are subject to the most restrictive sanctions
United States government sanctions
United_States_government_sanctions
Class of artificial neural network
maintains a hidden state—a form of memory that is updated at each time step based on the current input and the previous hidden state. This feedback mechanism
Recurrent_neural_network
Condition determining when a linear electronic circuit will oscillate
In electronics, the Barkhausen stability criterion is a mathematical condition to determine when a linear electronic circuit will oscillate. It was put
Barkhausen stability criterion
Barkhausen_stability_criterion
Science of air vehicle orientation and control in three dimensions
nose) In analyzing the stability of an aircraft, it is usual to consider perturbations about a nominal steady flight state. So the analysis would be
Aircraft_flight_dynamics
Electronic circuit that cuts power when voltage falls below its operating range
the input impedance of the regulator, an UVLO with a higher hysteresis should be used to prevent oscillations before settling down to a steady state and
Undervoltage-lockout
Control loop feedback mechanism
method to apply a large enough step-change input that the output can be measured; however, too large of a step change can affect the process stability. Additionally
PID_controller
When concentrations of molecules in a living cell or organ remain constant
Essentially, steady state can be thought of as homeostasis at a cellular level. Metabolic regulation achieves a balance between the rate of input of a substrate
Steady_state_(biochemistry)
Robust nonlinear control to achieve exponential stabilization
state, d ( x , t ) {\displaystyle d(x,t)} encapsulates modeling uncertainties and external disturbances, and u {\displaystyle u} is the control input
RISE_controllers
Overview of and topical guide to control engineering
uses sensors to measure the output performance of the device being controlled and those measurements can be used to give feedback to the input actuators
Outline of control engineering
Outline_of_control_engineering
Topics referred to by the same term
overall energy of the molecule and increase stability Nonlocal goto, an abstract representation of the control state of a computer program Nonlocal Lagrangian
Nonlocal
Type of machine learning model
user input. The generated instruction along with user input is then used as input to another instance of the model under a "Instruction: [...], Input: [
Large_language_model
Advanced method of process control
system inputs and provides the transfer function that will reduce the total error across the frequency spectrum, trading off state error against input frequency
Model_predictive_control
Oscillator with frequency controlled by a voltage input
a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform
Voltage-controlled_oscillator
Form of synaptic inhibition mediated by increased membrane conductance
conductance, which can decrease input resistance and the membrane time constant, causing coincident excitatory currents to be “shunted” but not necessarily
Shunting_inhibition
Loop that increases an initial effect
positive feedback is in phase with the input, in the sense that it adds to make the input larger. Positive feedback tends to cause system instability. When the
Positive_feedback
Four-wheel drive system developed by Mitsubishi Motors
acceleration and driving stability. The AWC-ECU is a computer that uses the inputs from various sensors to assess the state of vehicle stability and, if necessary
Mitsubishi_S-AWC
Checking software against expectations
of inputs and preconditions (initial state) is not feasible, even with a simple product. Defects that manifest in unusual conditions are difficult to find
Software_testing
Type of voltage converter circuit
galvanic isolation between the input and any outputs. The flyback converter is a buck–boost converter with the inductor split to form a transformer, so that
Flyback_converter
Graphical calculator used in electrical engineering
(z)<0} ) correspond to negative resistance, which is used for oscillator design and stability analysis. The display allows engineers to evaluate multiple
Smith_chart
Precision differential amplifier with input buffering
rejection ratio, and very high input impedances. Instrumentation amplifiers are used where great accuracy and stability of the circuit both short- and
Instrumentation_amplifier
Field of electrical engineering
A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals. Therefore
System_analysis
computational penalty due to the requirement to implicitly solve for the next system state. Finally, QSS methods satisfy remarkable global stability and error bounds
Quantized state systems method
Quantized_state_systems_method
Instructions for the x86 microprocessors
two possible orders of inputs (signed/unsigned and unsigned/signed) because VEX encoding only supports the second input operand to be a memory operand.
Advanced_Vector_Extensions
Tilting three-wheeled motor vehicle
input and the vehicle's speed to estimate the lateral acceleration and hence the appropriate tilt angle. The DTC system provides excellent stability at
CLEVER
Reaction that splits an atomic nucleus
fission energy." About 6 MeV of the fission-input energy is supplied by the simple binding of an extra neutron to the heavy nucleus via the strong force;
Nuclear_fission
Predictive filter
signal for the second state term is represented as part of the input signal vector u, otherwise the u vector is set to zero. Input coupling matrix B has
Alpha_beta_filter
Linear integrated circuit precision shunt regulator
capacitances to steady-state voltages takes up 0.5–1 μs more. Capacitive cathode loads (CL) may cause instability and oscillation. According to stability boundary
TL431
Smooth approximation of one-hot arg max
network to normalize the output of a network to a probability distribution over predicted output classes. The softmax function takes as input a tuple
Softmax_function
Power supply with switching regulator
yields an output voltage which is opposite in polarity to the input voltage. Other buck circuits exist to boost the average output current with a reduction
Switched-mode_power_supply
Process necessary for BJT amplifiers to work correctly
To ensure absolute stability of the amplifier, a stability factor of less than 25 is preferred, and so small-signal transistors have large stability factors
Bipolar_transistor_biasing
Method for converting signals between digital and analog
high-resolution digital input signal into a lower-resolution, but higher sample-frequency signal that may then be mapped to voltages and smoothed with
Delta-sigma_modulation
Voluntary or forced renunciation of sovereign power
maintain stability during political succession. Historically, abdications have occurred both by force (where the regnant was dethroned, thus forced to abdicate
Abdication
Electronic circuit
emitter-to-load resistors (if any present; these resistors set idle current of the output transistors, improve stability and decrease the input-output
Diamond_buffer
Type of feedforward neural network
in one direction from input to output with no cycles or loops. Unlike recurrent neural networks, which maintain internal state through feedback connections
Multilayer_perceptron
Property that an increasing voltage results in a decreasing current
one unstable state and one stable state. When in its stable state a pulse is applied to the input, the output switches to its other state and remains in
Negative_resistance
State-owned bank in Thailand
"Krungthai Bank loses state enterprise status". Bangkok Post. 12 November 2020. Retrieved 23 August 2026. "About KTB: Roots of Stability". Krungthai Bank.
Krungthai_Bank
Polish-Canadian scientist and professor (1934 - 1997)
Cite journal requires |journal= (help) Zames, G. (1996). "Input-output feedback stability and robustness, 1959-85". IEEE Control Systems Magazine. 16
George_Zames
American social networking service
human input to select representative tweets with context. In late 2009, the "Twitter Lists" feature was added, making it possible for users to follow
X_(social_network)
Mathematical concept
numerical stability associated with an algorithm serves to indicate the extent to which initial errors or perturbations present in the input data of the
Approximation_error
Algorithm in numerical analysis
has elements indexed input[1] to input[input.length]. for i = 1 to input.length do // c is zero the first time around. var y = input[i] - c // Alas, sum
Kahan_summation_algorithm
Algorithm for modelling sequential data
the multi-head attention mechanism, in which input data such as text, images, or audio is converted to a sequence of numerical representations called
Transformer_(deep_learning)
Commission developing diplomatic norms limiting cyber-offense
The Global Commission on the Stability of Cyberspace was a multistakeholder Internet governance organization, dedicated to the creation of diplomatic norms
Global Commission on the Stability of Cyberspace
Global_Commission_on_the_Stability_of_Cyberspace
Effect that limits performance of advanced atomic clocks
The Dick effect (hereinafter referred to as "the effect") is an important limitation to frequency stability for modern atomic clocks such as atomic fountains
Dick_effect
Mathematical descriptions of the properties of certain cells in the nervous system
the input stage to the probability of releasing neurotransmitter at the output stage. For a more detailed description of this model, see the Two state Markov
Biological_neuron_model
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INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
INPUT TO-STATE-STABILITY
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