M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

We propose and analyze additive preprocessing for computing the vectors in and bases for the null spaces of matrices. Instead of singular linear systems we solve nonsingular ones that preserve the conditioning properties and the structure of the input matrices. For ill conditioned input we can extend our preprocessing further, to decrease the problem size. Our approach is readily extended to th...

The analysis of control of linear multi-agent systems has recently emerged as an important domain that is receiving a lot of interest from a variety of research communities, and consensus plays a fundamental role in this field of study. We will show how using linear algebra techniques can be analyzed the consensus controllability problem for singular multi-agent systems, in which all agents hav...

This paper investigates the problem of state feedback H∞ control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H∞ controller for the singular delta operator system are presented. As s...

In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of ∆-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak ∆invariance are considered. They can be seen a...

The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized ...