ℋ_∞ model reduction for linear parameter-varying systems with distributed delay

Abstract

This paper is concerned with the ℋ_∞ model reduction for linear parameter-varying (LPV) systems with both discrete and distributed delays. For a given stable system, our attention is focused on the construction of reduced-order models, which approximate the original system well in an ℋ_∞ norm sense. First, a sufficient condition is proposed for the asymptotic stability with an ℋ_∞ performance of the error system by using the parameter-dependent Lyapunov functional method. Then, the decoupling technique is applied, such that there does not exist any product term between the Lyapunov matrices and the system matrices in the parametrised linear matrix inequality (PLMI) constraints; thus a new sufficient condition is obtained. Based on the new condition, two different approaches are developed to solve the model reduction problem. One is the convex linearisation approach and the other is the projection approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

Keywords:

• Distributed delay
• model reduction
• parameterised linear matrix inequality (PLMI)
• linear parameter-varying (LPV) systems

Acknowledgements

The authors wish to thank the associate editor and the reviewers for their valuable comments and suggestions, which have helped improve the presentation of the paper.