In this paper, we consider non-singular linear transformation of the inputand outputvariables in the Data Envelopment Analysis (DEA). The transformation is useful in selecting variables and dealing, for instance, with interval scale variables. We will develop general theory and show that the results are invariant due to non-singular linear transformation provided the concept of “dominance” is d...

This paper presents the control of non-regular or singular nonlinear systems applying non-linear predictive controllers. The systems treated here have the relative degree not well defined thus feedback linearization is not applicable due to singularities in the input-output linearizing control law. An alternative controller capable of dealing with non-regular systems is the NCGPC (Nonlinear Con...

This paper is devoted to the problem of H∞ output feedback control for linear singular systems with state time-varying delay. The purpose is to design a non-singular dynamic output feedback controller to ensure that the closed-loop system is regular, impulse free and stable with a prescribed H∞ performance level. Using the linear matrix inequality (LMI) approach, a new delay-dependent stability...

A new method of computation of singular values and left and right singular vectors of arbitrary nonsquare matrices has been proposed. The method permits to avoid solutions of high rank systems of linear equations of singular value decomposition problem, which makes it not sensitive to ill-conditioness of decomposed matrix. On base of Eckart-Young theorem, it was shown that each second order r-r...

Linear transformation techniques such as singular value decomposition (SVD) have been used widely to gain insight into the qualitative dynamics of data generated by dynamical systems. There have been several reports in the past that had pointed out the susceptibility of linear transformation approaches in the presence of nonlinear correla tions. In this tutorial review, the local dispersion alo...

In this paper, subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented. The proposed algorithms consist basically of two steps. The first one is a standard (linear) subspace algorithm applied to an equivalent linear system whose inputs (respectively outputs) are filtered (by the nonlinear functi...

Consider axisymmetric equations associated with Laplace-type operators. We establish full regularity estimates in high-order Kondrat′vetype spaces for possible singular solutions due to the non-smoothness of the domain and to the singular coefficients in the operator. Then, we show suitable graded meshes can be used in high-order finite element methods to achieve the optimal convergence rate, e...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

This paper concerns the robust H∞ filtering problem for discrete-time singular systems with norm-bounded uncertainties in all system matrices of state equations. On the basis of the admissibility assumption of the uncertain singular systems, a set of necessary and sufficient conditions for the existence of the desired filters is established, and a normal filter design method under the linear ma...

This paper deals with the optimal control problem that arise when a hydraulic system with fixed-head hydroplants is considered. In the frame of a deregulated electricity market the resulting Hamiltonian for such systems is linear in the control variable and results in an optimal singular/bang-bang control policy. To avoid difficulties associated with the computation of optimal singular/bang-ban...