State observers for nonlinear systems with smooth/bounded input

It is known that for nonlinear systems the driftobservability property (i.e. observability for zero input) is no t sufficient to guarantee the existence of an asymptotic observer for any input. Many authors studied conditions on systems structure that ensure uniform observability (i.e. observability for any input). Conditions are available that define restrict classes of uniformly observable systems. This work considers the problem of state observation with exponential error rate for smooth nonlinear systems that do no t meet conditions of uniform observability: conditions are given on the input, instead of on the system structure. It is shown that drift-observability, together with a smoothness/boundedness condition on the input, is sufficient to ensure the existence of an exponential observer. Three types of observers are presented, that can be constructed under driftobservability assumption.