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| | In [[nonlinear control]], the technique of ''Lyapunov redesign'' refers to the design where a stabilizing state feedback controller can be constructed with knowledge of the [[Lyapunov function]] <math>V</math>. Consider the system |
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| | :<math>\dot{x} = f(t,x)+G(t,x)[u+\delta(t, x, u)]</math> |
| | |
| | where <math>x \in R^n</math> is the state vector and <math>u \in R^p</math> is the vector of inputs. The functions <math>f</math>, <math>G</math>, and <math>\delta</math> are defined for <math>(t, x, u) \in [0, \inf) \times D \times R^p</math>, where <math>D \subset R^n</math> is a domain that contains the origin. A nominal model for this system can be written as |
| | |
| | :<math>\dot{x} = f(t,x)+G(t,x)u</math> |
| | |
| | and the control law |
| | |
| | :<math>u = \phi(t, x)+v</math> |
| | |
| | stabilizes the system. The design of <math>v</math> is called ''Lyapunov redesign''. |
| | |
| | == Further reading == |
| | * {{cite book |
| | | last = Khalil |
| | | first = H.K. |
| | | authorlink = Hassan K. Khalil |
| | | year = 2002 |
| | | edition = 3rd edition |
| | | url = http://www.egr.msu.edu/~khalil/NonlinearSystems/ |
| | | isbn = 0-13-067389-7 |
| | | title = Nonlinear Systems |
| | | publisher = [[Prentice Hall]] |
| | | location = Upper Saddle River, NJ}} |
| | |
| | == References == |
| | {{reflist}} |
| | |
| | [[Category:Nonlinear control]] |
In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge of the Lyapunov function . Consider the system
where is the state vector and is the vector of inputs. The functions , , and are defined for , where is a domain that contains the origin. A nominal model for this system can be written as
and the control law
stabilizes the system. The design of is called Lyapunov redesign.
Further reading
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