LMI approach to non-Lyapunov stability of discrete descriptor time delay systems

Abstract

The article provides sufficient conditions for the practical and finite time stability of linear singular continuous time delay systems fulfilling the following formulation: Ex(k+1)=A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> x(k)+A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> x(k-1). Analyzing the finite time stability concept, novel delay independent conditions have been presented. The conditions were derived using the linear matrix inequality (LMI) approach. The LMI method was based on the analysis of the Lyapunov-like functions and their properties within the subspace of consistent initial conditions. A novel sufficient delay-dependent criterion for the finite time stability based on the LMI approach has been established.