In this paper, we will analyze a basic class of diffusion adaptive filters based on least mean squares algorithms. Both stability and performance analyses will be carried out under a general cooperative information condition, without such stringent conditions as statistical independence and stationarity that have been used in almost all the existing literature and, thus, makes our theory applicable to stochastic systems with feedback. In comparison with the existing work, a key theoretical difficulty that needs to be overcome in this paper is to analyze the product of asymmetric correlated non-stationary random matrices, which is inherent in the structure of the diffusion-type filtering algorithms. We will further demonstrate that the distributed adaptive filters can estimate a dynamic process of interest from noisy measurements by a set of sensors working in a cooperative way, in the natural scenario where none of the sensors can fulfill the estimation task individually due to insufficient information. Finally, the necessity of our cooperative information condition will also be discussed in this paper.