奇异摄动系统正实性能分析

Positive Realness of Singularly Perturbed Systems

利用广义系统模型,通过改进已有的广义系统正实引理,讨论了奇异摄动系统的正实性判断问题。利用隐函数存在定理,基于代数Riccati等式讨论了当小参数趋于零时奇异摄动系统正实性与极限系统正实性之间的关系。进一步提出了根据极限系统对奇异摄动系统的正实性进行判断的判据。算例验证了结果的有效性,为在一定条件下对奇异摄动系统的正实性进行有效判断提供了一种新的方法。

To discuss the strictly positive realness judgment criteria of singularly perturbed systems, a singular system model is employed, and the existing positive real lemma of singular systems is improved. By applying the implicit function theorem the relationship between the positive realness of singularly perturbed system and that of its limit system is investigated based on the algebraic Riccati equation. Criteria are proposed to judge the positive realness of singularly perturbed system. A numerical example is given to prove the effectiveness of the criteria. The results provide novel criteria for the judgment of the positive realness of singularly perturbed systems under certain conditions.