Kharitonov定理的若干讨论

SOME DISCUSSIONS ON KHARITONOV'S THEOREM

Kharitonov 在区间多项式稳定性研究中的开创性工作,给鲁棒控制领域带来了新的希望.Kharitonov 定理断言,几个特殊多项式的稳定性即可保证某一族(无穷多个)多项式的稳定性.近年来,这一领域的研究引起了控制界的极大关注,出现了许多有意义的结果.在这些工作中,对 Kharitonov 定理本身也有一定的探讨.由于原始的定理证明不够直观明了,一些学者试图对定理的证明进行简化,得到了一些简单证明.

This paper presents some proofs of Kharitonov's theorem and its generalized version,andmakes some comparisons among them.By resorting to the concept of positive pair of polyno-mials,we give a quite simple proof of Kharitonov's theorem.We naturally verify the general-ized Kharitonov's theorem by introducing the so-called Kharitonov's combination.A Nyquist-typeproof of the generalized version is also given,which is the simplest proof appeared in litera-ture so far.The proofs of the generalized version can easily be reduced to the proofs of theoriginal theorem.These proofs provide some insights into the intrinsic characteristics ofKharitonov's theorem.