Abstract: Incremental design approach is widely used in software development practice，but few works studies the approach formally.This paper studies the incremental design approach formally with the polynomial dynamic system approach to software development.Firstly，an example is presented to show that the incremental design approach cannot be applicable to all cases.Then，a sufficient condition of incremental software design is introduced based on the concept of requirement’s heritability.That is all the requirements designed are heritable.

Key words: software cybernetics, supervisory control theories, polynomial dynamic systems, incremental software design, heritability

摘要： 增量式设计方法是软件开发中常用的一种设计方法，但是对其进行形式化研究的并不多。论文研究用多项式动态系统方法开发软件时是否可以用增量式设计方法。首先通过一个反例说明并不是在任何情况下都可以用增量式设计方法，然后通过定义软件需求的继承性，得到增量式软件设计的一个充分条件：当已经设计的软件需求具有继承性时，可以对新的软件需求采用增量式设计。

关键词: 软件控制论, 监控理论, 多项式动态系统, 增量式软件设计, 继承性