Control-Lyapunov function
In control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function to systems with control inputs. The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means that if the system starts in a state in some domain D, then the state will remain in D for all time. For asymptotic stability, the state is also required to converge to . A control-Lyapunov function is used to test whether a system is asymptotically stabilizable, that is whether for any state x there exists a control such that the system can be brought to the zero state asymptotically by applying the control u.
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- enIn control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function to systems with control inputs. The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means that if the system starts in a state in some domain D, then the state will remain in D for all time. For asymptotic stability, the state is also required to converge to . A control-Lyapunov function is used to test whether a system is asymptotically stabilizable, that is whether for any state x there exists a control such that the system can be brought to the zero state asymptotically by applying the control u.
- Has abstract
- enIn control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function to systems with control inputs. The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means that if the system starts in a state in some domain D, then the state will remain in D for all time. For asymptotic stability, the state is also required to converge to . A control-Lyapunov function is used to test whether a system is asymptotically stabilizable, that is whether for any state x there exists a control such that the system can be brought to the zero state asymptotically by applying the control u. The theory and application of control-Lyapunov functions were developed by and Eduardo D. Sontag in the 1980s and 1990s.
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- Control-Lyapunov function
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- enControl-Lyapunov function
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- books.google.com/books%3Fid=_eTb4Yl0SOEC%7Caccessdate=2009-03-04
- www.sontaglab.org/FTPDIR/sontag_mathematical_control_theory_springer98.pdf
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- Artstein's theorem
- Autonomous system (mathematics)
- Category:Stability theory
- Controllability
- Control system
- Control theory
- Differentiable function
- Drift plus penalty
- Dynamical system
- Eduardo D. Sontag
- Francis Clarke (mathematician)
- Inner product
- Lie derivative
- Lyapunov function
- Lyapunov optimization
- Lyapunov stability
- Optimization (mathematics)
- Zvi Artstein
- SameAs
- 4iL7Z
- m.0fv3sh
- Q5165805
- 控制李亞普諾夫函數
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- Category:Stability theory
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- Control-Lyapunov function?oldid=1117887432&ns=0
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