Lyapunov stability of adaptive LMS array

The adaptive least mean square (LMS) array, particularly an array using reference signal reproduction processor (RSRP), is analyzed based on investigations of Lyapunov stability properties for the array weighting. The operation of the array utilizing RSRP is formulated as a Volterra integrodifferential equation. It is assumed as an essential condition that zero input to RSRP implies zero output. This condition makes the equation homogeneous and leads to an important result that the trivial solution for the equation has the Lyapunov asymptotic stability. Namely, the weighting for the array with RSRP might be drived to zero asymptotically. The servomechanism viewpoint also provides an intuitive understanding for the result.