均方稳定的多维AR系统的一个性质

PROPERTY OF MULTIDIMENSIONAL AR SYSTEMS BEING STABLE IN MEAN SQUARE

ARX系统的随机适应控制常导致其闭环稳态 AR系统的均方稳定性 .在噪声满足一定的矩条件下 ,证明了若多维 AR系统 A( z) yk=wk 在下列意义下均方稳定 :lim supn→∞1n ∑nk=1‖yk‖ 2 <∞ a.s.则 det A( z)不可能有爆炸的根 ,即 det A( z)的零点全在单位圆上或圆外 .

Stochastic adaptive stabilization of ARX system usually leads to the resulting system being stable in the mean square. Imposing certain conditions on the noise, this paper proves that multidimensional AR system A(z)y k=w k being stable in the mean square, by which it is meant that the long run average of the squared output is bounded: lim sup n→∞1n ∑nk=1‖ y k‖ 2<∞ , hasn't any explosive roots, i.e., all roots of det A(z) are on or outside the unit circle.