Zames–Falb multipliers
E580592
Zames–Falb multipliers are a class of frequency-domain operators used in control theory to analyze and guarantee the stability of nonlinear and time-varying feedback systems.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
class of operators
ⓘ
control theory concept ⓘ |
| appliesTo |
Lur’e-type systems
ⓘ
multi-input multi-output systems ⓘ nonlinear feedback systems ⓘ single-input single-output systems ⓘ time-varying feedback systems ⓘ |
| associatedWith |
sector-bounded nonlinearities
ⓘ
slope-restricted nonlinearities ⓘ |
| assumes |
bounded memory nonlinearities
ⓘ
causal feedback interconnections ⓘ |
| basedOn | integral quadratic constraints ⓘ |
| characterizedBy |
bounded L1 impulse responses
ⓘ
causal linear time-invariant operators ⓘ positivity conditions in frequency domain ⓘ |
| constraintType | integral inequality constraints ⓘ |
| domain | frequency domain ⓘ |
| ensures | input-output stability under specified nonlinearities ⓘ |
| field | control theory ⓘ |
| generalizes | classical multiplier methods in absolute stability ⓘ |
| goal | derive frequency-domain stability inequalities ⓘ |
| introducedBy |
George Zames
NERFINISHED
ⓘ
Peter L. Falb NERFINISHED ⓘ |
| involves | frequency-dependent weighting of signals ⓘ |
| mathematicalForm |
convolution operators in time domain
ⓘ
multiplicative frequency-domain transfer functions ⓘ |
| purpose | guarantee stability of feedback systems ⓘ |
| relatedTo |
IQC multipliers
ⓘ
L2-gain analysis ⓘ Popov criterion ⓘ absolute stability ⓘ circle criterion ⓘ passivity theory ⓘ small-gain theorem NERFINISHED ⓘ |
| typicalProperty | nonnegative real part over frequency range ⓘ |
| usedFor |
performance analysis of nonlinear systems
ⓘ
robust stability margins ⓘ |
| usedIn |
analysis of dead-zone nonlinearities
ⓘ
analysis of relay nonlinearities ⓘ analysis of saturation nonlinearities ⓘ nonlinear control ⓘ robust control design ⓘ stability analysis ⓘ time-varying systems analysis ⓘ |
| usedToDerive | sufficient conditions for stability ⓘ |
| usedWith |
Bode plots
ⓘ
Nyquist plots NERFINISHED ⓘ |
Referenced by (1)
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