Stability theory

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. The theory and application of control-Lyapunov functions were developed by and Eduardo D. Sontag in the 1980s and 1990s. (Wikipedia).

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Related pages

Lyapunov stability | Control theory | Lyapunov function | Drift plus penalty | Lyapunov optimization | Dynamical system | Lie derivative | Control system | Artstein's theorem | Differentiable function | Controllability | Autonomous system (mathematics)