Adaptive control is a very appealing technology, at least in principle. Yet its use has been conditioned by an attitude of distrustfulness on the part of some practitioners. In this paper, we explain why such distrustfulness is warranted, by reviewing a number of adaptive control approaches which have proved deficient for some reason that has not been immediately apparent. The explanation of the deficiencies, which normally were reflected in unexpected instabilities, is our main concern. Such explanations, coupled with remedies for avoiding the deficiencies, are necessary to engender confidence in the technology. These include the unpredictable failure of the MIT rule; the bursting phenomenon, and how to prevent it; the Rohrs' counterexample, which attempted to disqualify all adaptive control algorithms; the notion that identification of a plant is only valid conceptually for a restricted range of controllers (with the implication that in adaptive control, certain controller changes suggested by adaptive control algorithms may introduce instability); and the concept of multiple model adaptive control.

The discrete Hartley transforms (DHT) of types I -- IV and the related matrix algebras are discussed. We prove that any of these DHTs of length $N=2^t$ can be factorized by means of a divide--and--conquer strategy into a product of sparse, orthogonal matrices where in this context sparse means at most two nonzero entries per row and column. The sparsity joint with orthogonality of the matrix factors is the key for proving that these new algorithms have low arithmetic costs equal to $\frac52 N\log_2 (N)+O(N)$ arithmetic operations and an excellent normwise numerical stability. Further, we consider the optimal Frobenius approximation of a given symmetric Toeplitz matrix generated by an integrable symbol in a Hartley matrix algebra. We give explicit formulas for computing these optimal approximations and discuss the related preconditioned conjugate gradient (PCG) iterations. By using the matrix approximation theory, we prove the strong clustering at unity of the preconditioned matrix sequences under the sole assumption of continuity and positivity of the generating function. The multilevel case is also briefly treated. Some numerical experiments concerning DHT preconditioning are included.

In this paper a methodology to cluster time series based on measurement data is described. In particular, we propose a distance for stochastic models based on the concept of subspace angles within a model and between two models. This distance is used to obtain a clustering over the set of time series. We show how it is related to the mutual information of the past and the future output processes, and to a previously defined cepstral distance. Finally, the methodology is applied to the clustering of time series of power consumption within the Belgian electricity grid.

We present a novel full-rate full-diversity orthogonal space-time block code for QPSK modulation and $4$ transmit antennas based on quaternionic algebra. The code does not result in constellation expansion unlike other full-rate full-diversity codes in the literature. The quaternionic structure of the code is exploited to reduce the complexity of maximum likelihood (ML) coherent decoding from a size-$256$ search to a size-$16$ search. Furthermore, we show how to modify this low-complexity coherent ML decoding rule to derive a non-coherent differential ML decoding rule. Due to the orthogonality of the code, ML differential decoding results in the minimum SNR loss of $3$ dB from coherent ML decoding. Finally, extensive simulation results in a WiMAX 802.16 broadband wireless access environment demonstrate that the proposed code increases the cell coverage area by $1.5$ and $2.6$ folds compared to single-antenna transmission at $10^{-3}$ bit error rate when combined with $1$ and $2$ receive antenna(s), respectively.

We present a computationally-efficient matrix-vector expression for the solution of a matrix linear least squares problem that arises in multistatic antenna array processing. Our derivation relies on an explicit new relation between Kronecker, Khatri-Rao and Schur-Hadamard matrix products, which involves a selection matrix (i.e., a subset of the columns of a permutation matrix). Moreover, we show that the same selection matrix also relates the vectorization-by-columns operator to the diagonal extraction operator, which plays a central role in our computationally-efficient solution.

In the framework of BIBO stability tests for one-dimensional (1-D) linear systems, the Schur-Cohn stability test has the appealing property of being a recursive algorithm. This is a consequence of the simultaneously algebric and analytic aspect of the Schur coefficients, which can be also regarded as \textit{reflection coefficients. } In the multidimensional setting, this dual aspect gives rise to two extension of the Schur coefficients that are no longer equivalent. This paper presents the two extensions of the Schur-Cohn stability test that derive from these extended Schur coefficients. The reflection-coefficient approach was recently proposed in the 2-D case as a necessary but non sufficient condition of stability. The Schur-type multidimensional approach provides a stronger condition of stability, which is necessary and sufficient condition of stability for multidimensional linear system. This extension is based on so-called slice function associated to $n$-variable analytic functions. Several examples are given to illustrate this approach.