In many cases of interest, systems described by non-linear differential equations are modelled by linear equations for purposes of synthesizing feedback controllers. A theorem relating the stability properties of the linear model and the non-linear system is presented and discussed.
Bibliographical noteFunding Information:
t Communicated by the Author. This research was partially supported by N.S.F. Grant GK-3273 and A.F.O.S.R. Grant 66-0704C. t The vector norm IIzll = <I?-IZ(2)112 where z, is the ith component of z. The associated matrix norm B = (I~I I?_llb" 12)112 where the b,,'s are the elements of B.