The stability property of LMS algorithm (least mean square algorithm) and the design of robust LMS algorithm are discussed in this paper.The standard LMS algorithm is transferred into a standard state equation form of discrete-time system.Then its quadratic stability property is analyzed by linear matrix inequality technique.Owning to the noise often emerging in input and measure of filter

a robust LMS algorithm

in which convergence

robust stability and robust property are all considered

is developed.In the end

simulation results are presented to support the analysis and to compare the performance of the robust algorithm with the usual LMS algorithm.They show that the algorithm is feasible.