LMI Tests for Positive Definite Polynomials: Slack Variable Approach

Real and complex variable positive definite functions

In this paper we present an overview of the implications of our previously derived results for positive definite kernels on the general theory of positive definite functions. We begin by exploring the consequences of a set of differential inequalities on the global behaviour of a smooth positive definite function of one real variable. Then we propose a natural extension of this study to the com...

Fast algorithms for positive definite matrices structured by orthogonal polynomials

Positive definite matrices structured by orthogonal polynomial systems allow a Cholesky type decomposition of their inverse matrices in O(n2) steps. The algorithm presented in this paper uses the three-term recursion coefficients and the mixed moments of the involved polynomials.

Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices

Positive Definite and Semi-definite Splitting Methods for Non-hermitian Positive Definite Linear Systems

In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse nonHermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove th...

An LMI approach to checking stability of 2D positive systems

Abstract. Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtai...