A generalization of Sullivan inequality on the ratio of the probability of a linear code to that of any of its cosets is proved. Starting from this inequality, a sufficient condition for successful decoding of linear codes by a probabilistic method is derived. A probabilistic decoding algorithm for “low–density parity–check codes” is also analyzed. The results obtained allow one to estimate exp...

The linear multiplicative programming problem minimizes a product of two (positive) variables subject to linear inequality constraints. In this paper, we show NP-hardness of linear multiplicative programming problems and related problems.

This paper considers interval time-varying delay systems. The time-delay interval is divided into several zones and the systems switch among the different zones. Based on LyapunovKrasovskii functional methods and linear matrix inequality (LMI) techniques, Exponential stability is exploited for every time-delay zone. The global stability of the switched system is guaranteed if some minimum avera...

We construct non-linear information inequalities from Matúš’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they ...

This paper deals with several challenging problems of robust filtering for two-dimensional (2-D) systems. First of all, new linear matrix inequality (LMI) characterizations for the and 2 norms of 2-D systems are introduced and thoroughly established. Based on these preparatory results, convex (LMI) characterizations for robust , 2, and robust mixed 2 filtering are derived. The efficiency and vi...

This paper presents a study on the recently proposed linear inequality representation of Arrovian Social Welfare Functions (ASWFs). We correct and show several sufficient conditions on preference domains for the linear inequalities of the representation to form integral polytopes. We also show that a given probabilistic ASWF induces a real vector satisfying the inequalities.

We describe a Farkas-type condition for strong solvability of interval linear inequalities. The result is used to derive several descriptions of the set of strong solutions and to show that this set forms a convex polytope.

In this paper, we propose a concept of polynomiality for variational inequality problems and show how to find a near optimal solution of variational inequality problems in a polynomial number of iterations. To establish this result we build upon insights from several algorithms for linear and nonlinear programs (the ellipsoid algorithm, the method of centers of gravity, the method of inscribed ...

This paper provides an exact linear matrix inequality (LMI) condition for robust asymptotic stability of uncertain systems depending polynomially on a scalar parameter in both continuous-time and discrete-time cases. Specifically, this condition exploits sum of squares (SOS) techniques and is based on the construction of polynomials of known degree that detect the presence of eigenvalues on the...

This paper is concerned with a robust observer design for linear time-delay systems via linear matrix inequality approach. The proposed method not only guarantees the stability of the proposed observer, but also reduces the effects of different unstructured uncertainties on the estimated error.