Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance matrices), which are necessary taking in mind practical aspects of the nonlinear treatment of the least-squares estimation problem. The algorithms are examined for different higher-order and non-Gaussian processes (time-series) and an impact of signal properties on covariance matrices is analysed.
In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation ∆(xn = pnxτ(n)) + f(n, xσ(n)) = qn are obtained. Examples are included to illustrate the results.
In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form ∆ 2 (r(n)∆2 (y(n) + p(n)y(n − m))) + q(n)G(y(n − k)) = 0 is studied under the assumption ∑∞ n=0 n ⁄ r(n) < ∞. New oscillation criteria have been established which generalize some of the existing results in the literature.