The discrete Fourier transform (DFT) is used for determining the coefficients of a transfer function for n-order singular linear systems, Ex = ∑n i=1 Aix (n−1) + Bu, where E may be singular. The algorithm is straight forward and easily can be implemented. Three step-by-step examples illustrating the application of the algorithm are presented.

This paper addresses the problem of finite-time H∞ filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochastic H∞ finitetime boundedness are presented. Then, the H∞ filtering is designed for the class of singular stochastic system...

A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.

We present optimal, up to poly-logarithmic factors, bit complexity results for basic operations, matrix-vector multiplication and solving non-singular linear systems, with structured matrices.

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...