In control theory, a control-Lyapunov function (CLF)[1][2][3][4] 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 Zvi Artstein and Eduardo D. Sontag in the 1980s and 1990s.
- ^ Isidori, A. (1995). Nonlinear Control Systems. Springer. ISBN 978-3-540-19916-8.
- ^ Freeman, Randy A.; Petar V. Kokotović (2008). "Robust Control Lyapunov Functions". Robust Nonlinear Control Design (illustrated, reprint ed.). Birkhäuser. pp. 33–63. doi:10.1007/978-0-8176-4759-9_3. ISBN 978-0-8176-4758-2. Retrieved 2009-03-04.
- ^ Khalil, Hassan (2015). Nonlinear Control. Pearson. ISBN 9780133499261.
- ^ Sontag, Eduardo (1998). Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition (PDF). Springer. ISBN 978-0-387-98489-6.