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This brief proposes a novel discrete-time realization of the spatial repetitive controller topology, an internal model principle-based regulator, which deals with the exogenous position-dependent periodic signals. A simple procedure is proposed in order to estimate the time-varying delay required to implement this spatial controller, resulting in a single recursive equation. A robust synthesis methodology based on a convex optimization problem constrained by linear matrix inequalities is also presented in order to guarantee the closed-loop system stability and performance in the presence of uncertain plant dynamics. The proposed design and implementation methods are validated on a direct current motor subject to angle-dependent disturbances.

Orthogonal subspace projection (OSP) has found many applications in hyperspectral data exploitation. Its effectiveness and usefulness result from implementation of two stage processes, i.e., annihilation of undesired signal sources by an OSP via inverting a matrix in the first stage followed by a matched filter to extract the desired signal source in the second stage. This paper presents a theory of recursive OSP (ROSP) for hyperspectral imaging, which performs OSP recursively without inverting undesired signature matrices. This ROSP opens up many new dimensions in extending OSP. First of all, ROSP allows OSP to implement varying signatures via a recursive equation without reinverting undesired signature matrices. Second, ROSP can be further used to derive an unsupervised ROSP (UROSP) OSP, which allows OSP to find a growing number of unknown signal sources recursively while simultaneously determining a desired number of signal sources. As a result, the commonly used automatic target generation process (ATGP) can be extended to a recursive ATGP, which can be considered as a special case of UROSP. Third, for practical applications, UROSP can be also extended in two differ ent fashions to causal process and progressive process, which give rise to causal UROSP and progressive UROSP, respectively, both of which can be easily realized in hardware implementation. Finally, UROSP provides a feasible stopping rule via a recently developed UROSP-specified virtual dimensionality.

This paper discusses the design and practical implementation of solving an external consensus problem for inhomogeneous networked multiagent systems with constant network delay in the output feedback. Based on the recursive equation, a novel prediction strategy is proposed using the transfer function form to overcome the effects of the network delay. By considering a single-input single-output linear system for each agent, the proposed strategy is simulated, demonstrated, and validated through a test-rig application. Concurrently, the stability of the control scheme and the criterion to determine the appropriate coupling gains value for the proposed consensus protocol are also studied.

We present a time-varying coefficient difference equation representation for sinusoidal signals with time-varying amplitudes and frequencies. We first obtain a recursive equation for a single chirp signal. Then, using this result, we obtain time-varying coefficient difference equation representations for signals composed of multiple chirp signals. We analyze these equations using the skew-shift operators. We show that the phases of the poles of the difference equations produce instantaneous frequencies (IF), and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes (IA). Then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation. The first algorithm we propose is based on the skew-shift operators. Next we derive the conditions under which we can use the so-called frozen-time approach. We propose an algorithm for IF and IA estimation based on the frozen-time approach. Then we propose an automatic signal separation method. Finally, we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods.

This paper describes a recursive computational algorithm for computing spectral factors of continuous-time and discrete-time power spectrum matrices. The matrices need not be positive definite. Convergence rates of the recursive equation are studied.

An analytic model for the reliability evaluation of hypercube multicomputers is presented. The model is based on the decomposition principle, where a hypercube of a higher dimension is recursively decomposed into smaller hypercubes, until the reliability of the smallest cube is modeled exactly. The reliability of the large n-cube is then obtained from this smallest base model using a recursive equation. The reliability model used is task-based, i.e., it is assumed that the system is operational if a task can be executed on the system. Analytic results are given for n-dimensional hypercubes with up to 75% system degradation. The model is validated by comparison of analytic results with simulation results. >

We derive the method of maximum entropy spectrum estimation by bordering techniques of linear algebra. Using bordering, we obtain the recursive solution to the Yule-Walker equations and the recursive equation for the Toeplitz determinant in terms of the partial correlation coefficients. Minimization of the forward and backward predictor errors is then done with respect to the partial correlation coefficients. The minimization is done stagewise, constraining higher partial correlation values to zero. Thus, the minimization is done for a maximum-entropy normal process; the Toeplitz determinant is a maximum.

The equalized-error ("EE") training procedure, introduced in this paper, is a new nonparametric training procedure for linear classifiers in a multiple-feautre stochastic environment. This procedure is a form of stochastic approximation that minimizes the sum of the expected normalized first moments of the fasely classified pattern vectors about the decision hyperplane. This sum is the "EE loss function." The minimization is achived by a simply implemented recursive equation. We show that the sequence of decision hyperplanes generated by this recursive equation converges in mean square and with probability one to a hyperplane that minimizes the EE loss function. We provide premiliminary qualitative and quantitative evidence that the EE training procedure converges rapidly and achives low asymptotic error probabilities over a wide range of overlapping pairs of class densities and nonlinearly separable pairs of class densities.

Two Convariance lower bounds for nonlinear state estimation problems are presented. These bounds are based upon the Cramer-Rao bound for treating nuisance parameters and they can be applied to filtering, smoothing, and prediction problems. The tightness of these bounds are examined using a nonlinear system where the recursive equation for covariance computation can be obtained. These results are also compared with the bound of Bobrovsky and Zakai.

A consecutive-k cycle is a circular system such that the system fails if and only if any i consecutive components all fail. Reliabilities for consecutive-k cycles are usually computed by recursive equations. However, most recursive equations proposed so far for the cycle involve reliabilities for consecutive-k lines, requiring two passes where the first pass computes only the line reliabilities. A recursive equation involving cycles only is proposed that is simpler in form but much harder to understand on intuitive grounds. Another advantage is that the proposed cycle recursion has the same form as a line recursion previously proposed. Thus a uniform treatment of lines and cycles is possible. This uniform approach is used to obtain some explicit solutions of both line and cycle reliabilities for 2 >

A multiple-line function, subprogrammed in Basic language on a microcomputer, has the ability to reference itself recursively. This feature is particularly useful in computing nontrivial recursive equations.