In recent years many authors pointed out that for non- linear systems the property of state observability for zero input (drift-observability) does not imply observ- ability for any input (uniform observability). This pa- per considers the problem of state observation for sys- tems that do not satisfy the restrictive condition of uni- form observability. In a previous work the authors have shown that drift-observability ensures existence of ex- ponential observers if the input function is sufficiently small. In this work a condition weaker than uniform observability (denoted almost-uniform observability) is found for existence of exponential observers in those cases in which the input is bounded and its derivative is sufficiently small (slowly varying input). The ob- server for small inputs and the observer for small input derivative are both presented in this paper. Numerical results show the effectiveness of the proposed observers.
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