Analysis of linear parameter‐varying systems using a non‐smooth dissipative systems framework

Abstract

AbstractThis paper presents new finite‐dimensional linear matrix inequality formulations for several important analysis problems of linear parameter‐varying systems. The approach is based on a non‐smooth dissipative systems framework using a continuous, piecewise‐affine parameter‐dependent Lyapunov function. The new analysis approach yields guaranteed and less conservative results than previously published techniques that are based on affine parameter‐dependent Lyapunov functions or Luré–Postnikov Lyapunov functions. Conservatism is reduced in this new approach because the analysis uses a more general class of parameter‐dependent Lyapunov functions (PDLFs). The new approach also provides an explicit trade‐off between conservatism and computational effort of the analysis technique. Note that, in contrast to the gridding approach typically used to develop a computationally feasible algorithm, this proposed approach guarantees the analysis results. This paper also shows that the numerical results of our approach, while computationally intensive, could be used to develop many new insights into the selection of PDLFs in the other analysis techniques. Copyright © 2002 John Wiley & Sons, Ltd.