There is no absolute answer that works for all types. But, you could use a TypeConverter instead of Convert, it usually works better. For example, there is a TimeSpanConverter:

public void Update<T>(string fieldName, string fieldValue)
{
    System.Reflection.PropertyInfo propertyInfo = typeof(T).GetProperty(fieldName);
    Type propertyType = propertyInfo.PropertyType;

    TypeConverter converter = TypeDescriptor.GetConverter(type);
    if (converter.CanConvertFrom(typeof(string)))
    {
        var a = converter.ConvertFrom(fieldValue, type);
        ...
    }
}