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This paper presents new sufficient conditions for state and fault estimation of nonlinear systems. A new approach is proposed to deal with unmeasured premise variables and corrupted outputs. The adopted observer strategy consists of a scheduled gain that depends only on the estimated outputs provided by the observer. The design of such scheduled gain follows from a technical rewriting of the state error and uses the Lyapunov framework to derive sufficient conditions written as linear matrix inequalities. Such conditions are less conservative than existing approaches that deal with unmeasured premise variables. The effectiveness of the developed approach is assessed through a numerical single‐link robotic arm and on a real car‐based experimental setup available at the laboratory. [ABSTRACT FROM AUTHOR]