关于直接调节系统的绝对稳定性

<正> 非线性自动调节系统的绝对稳定性问题最初是由讨论飞机自动驾驶仪引起的.它的一般化是讨论带有一个非线性执行机构的系统

ON THE ABSOLUTE STABILITY OF DIRECT CONTROL SYSTEM

Consider the absolute stability of direct control system: x=Ax + bf(σ), σ=c'x, (·)=d/dt.(1) We point out an error of A.I. Lurie, I.G. Malkin and A. M. Letev and an error in "Non-linear differential equations of higher order" by R. Reissig, G. Sansone and R. Conti.(2) We give the following result: Under the assumption that A is stable, the necessary and suffieient conditions for to satisfy the condition of the LBK Theorem and hence guarantee the absolute stability is that there exists a matrix B>0, such that(i) u(x) = x'Bx-(c'A + 2b'P)x-c'b≥0 for c′x=0,(ii) c'B~(-1)(c'A + 2b'P)≤0, where P is determined by the Lipunov relation A'P + PA = -B.(3) Consider the systems in the canonical form We give a criterion for the absolute stability.