In this paper, the problem of state observation with exponential error deca
y for nonlinear systems affine in the input is considered and an observer i
s proposed. For such an observer, the drift-observability property of the s
ystem (i.e,, observability for zero input), together with an assumption on
the input amplitude or on the observation relative degree, are sufficient c
onditions for exponential convergence of the observation error. The existen
ce of an exponential observer is correlated to the existence of a solution
for an H-infinity Riccati-like inequality. Global and semiglobal convergenc
e results are presented.