Lyapunov redesign

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 $V$. Consider the system

:$dot\{x\}\; =\; f(t,x)+G(t,x)\; [u+delta(t,\; x,\; u)]$

where $x\; in\; R^n$ is the state vector and $u\; in\; R^p$ is the vector of inputs. The functions $f$, $G$, and $delta$ are defined for $(t,\; x,\; u)\; in\; [0,\; inf)\; imes\; D\; imes\; R^p$, where $D\; subset\; R^n$ is a domain that contains the origin. A nominal model for this system can be written as

:$dot\{x\}\; =\; f(t,x)+G(t,x)u$

and the control law

:$u\; =\; phi(t,\; x)+v$

stabilizes the system. The design of $v$ is called "Lyapunov redesign".

References

* H. K. Khalil, "Nonlinear Systems," third edition, Prentice Hall, Upper Saddle River, New Jersey, 2002.