Lyapunov redesign explained

V . Consider the system• 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 ) x D x R ^{p} , where D \subset R ^{n} is a domain that contains the origin. A nominal model for this system can be written as• 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.

Further reading

• Book: Khalil , H.K. . Hassan K. Khalil

. Hassan K. Khalil . 2002 . 3rd . Nonlinear Systems . 0-13-067389-7 . . Upper Saddle River, NJ.