多调节机构的直接控制系统的绝对稳定性

Absolute Stability for Direct Control System of Multiadjustment Mechanism

本文继续文〔1〕的工作,讨论多调节机构的直接控制系统的绝对稳定性.§1给出m 个调节机构的直接控制系统判别其绝对稳定性的一个准则;§2就m=2的情形将其削别准则化为不等式条件,从而消去了待定的参数;§3则就一般情形给出了判别系统绝对稳定的一系列不等式条件.

This paper is a succession of the works in[1].In this paper we consider thedirect control system of multiadjustment mechanism.x(?)=Ax+Bφ(σ),σ=C^(T)x,(A a stable n×n matrix)φi(0)=0,0≤σi φi(σi)≤ki σ_i^2 (*)By using the Liapunov functionV(x)=x^T Hx+2∑βi∫_0^(σi)φi(σi)dσi,(H=H^T>0,βi≥0)we prove the sufficient condition of absolute stability of system(*)is threeexists a positive definite symmetric matrix G and parameters λi>0(i=1,2,…,m)such that the symmetric matrixΛMΛ+ΛN+NΛ+L (**)is positive definite.Further,we discuss the case of m=2 in detail.We prove that the condition formatrix(**)can be transformed into the condition for inequality and find theexistence interval of λ_1,λ_2.Therefere,the criterion of absolute stability of system(*)in the case m=2 is solved.For the general case,we give a condition for inequality of finding λi(i=1,2,…,m)which assures the system(*)to be absolute stable.