A method for adaptive estimation of ARMA processes

When the noise process in adaptive identification of linear stochastic systems is correlated, and can be represented by a moving average model, extended least squares algorithms are commonly used, and converge under a strictly positive real (SPR) condition on the noise model. In this paper, we present an adaptive algorithm for the estimation of autoregressive moving average (ARMA) processes, and show that it is convergent without any SPR condition, and has a convergence rate of O({loglog t)/t}^1/2).     

On the solvability of the positive real lemma equations

In this paper, we consider the classical equations of the positive real lemma under the sole assumption that the state matrix A has unmixed spectrum: σ(A)∩σ(−A)=. Without any other system-theoretic assumption (observability, reachability, stability, etc.), we derive a necessary and sufficient condition for the solvability of the positive real lemma equations.