Discussion on: "H∞ Control of Distributed and Discrete Delay Systems via Discretized Lyapunov Functional"

Abstract

performance requirement, and design of state feed-backcontrol.Asisnowwellknown,inordertoobtainstability conditions using Lyapunov-Krasovskiifunctional (LKF) approach, it is necessary to use acomplete quadratic LKF, as is done in this article. Asa general quadratic functional involve infinite numberof parameters, some discretization process is neces-sary in order to render conditions in a computableform. A piece-wise linear parameterization such aswidely used in finite element methods seems to be themost natural. However, there is a fundamental dif-ference between these two discretizations: in finiteelement analysis, the objective is purely to approx-imate the solution; in the discretization of LKF, it isalso necessary to guarantee the satisfaction of quad-raticinequalities.Therefore,thediscretizationofLKFis a much more sophisticated process.