This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

This paper presents a generalization of incremental condition estimation, a technique for tracking the extremal singular values of a triangular matrix. While the original approach allowed for the estimation of the largest or smallest singular value, the generalized scheme allows for the estimation of any number of extremal singular values. For example, we can derive estimates for the three smal...

In this paper, we present a GPU-accelerated implementation of randomized Singular Value Decomposition (SVD) algorithm on a large matrix to rapidly approximate the top-k dominating singular values and correspondent singular vectors. The fundamental idea of randomized SVD is to condense a large matrix into a small dense matrix by random sampling while keeping the important information. Then perfo...

A method for finding the optimal control of singular system with a quadratic cost functional using block pulse function is discussed. After introducing block pulse function in the beginning we develop an operational matrix for solving singular state equations. A numerical example is included to demonstrate the validity and applicability of the technique. Keywords— Optimal control, Singular syst...

This communication describes some image-compression concepts such as the transmitted energy of the digital signal and the relative error of the compressed image in function of the number and magnitude of the singular values used in the Singular Value Decomposition of the matrix that represents the original picture. Comparisons are made with wavelet-based techniques using a test image. Key-Words...

Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations Ax = 0 for the 0-1 adjacency matrix A. A graph G is singular of nullity η(G) ≥ 1, if the dimension of the nullspace ker(A) of its adjacency matrix A is η(G). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgra...

We extend the Golub-Kahan algorithm for computing the singular value decomposition of bidiagonal matrices to triangular matrices R. Our algorithm avoids the explicit formation of R T R or RRT. We derive a relation between left and right singular vectors of triangular matrices and use it to prove monotonic convergence of singular values and singular vectors. The convergence rate for singular val...

In this paper, we are discuss about the issue of synchronization for singular complex dynamical networks with Markovian jumping parameters and additive time-varying delays through pinning control by Takagi-Sugeno (T-S) fuzzy theory.The complex dynamical systems consist of m nodes and the systems switch from one mode to another, a Markovian chain with glorious transition probabili...

This paper describes a computational method for improving the accuracy of a given singular value and its associated left and right singular vectors. The method is analogous to iterative improvement for the solution of linear systems. That is, by means of a low-precision computation, an iterative algorithm is applied to increase the accuracy of the singular value and vectors; extended precision ...