Stability of random linear equations with applications

Stability problems of random linear equations arise naturally in many areas of engineering sciences, especially in the areas of automatic control and signal processing. The performance of many adaptation algorithms depends essentially on stability of certain random time-varying equations. As is well-known, in the time-varying case, general stability results are hard to find even in the case where the coefficient matrices are deterministic. This paper presents some theoretical results established in the past few years on time-varying random linear equations with some refinements and extensions, which have direct applications in adaptive estimation. Both pathwise asymptotic stability and stochastic exponential stability results are included