Lyapunov-Based Methods for Perturbed Continuous-Time Systems

Abstract

The matrix U denotes a positive matrix if each entry U_ij > 0 ∀i, j . A matrix is termed positive definite if it has properties in what is to follow. A square matrix Q is positive definite if

$${{\rm{x}}^T}Qx > 0{\rm{ }}\forall {\rm{x}} \ne {\rm{0}}$$

(13.1)

and positive semidefinite (non-negative definite) if

$${{\rm{x}}^T}Qx \ge 0{\rm{ }}\forall {\rm{x}}$$

(13.2)