Hankel-norm model approximation for LPV systems with parameter-varying time delays

Abstract

This article is concerned with Hankel-norm model approximation (HNMA) for linear parameter-varying systems with parameter-varying time delays. For a given stable system, our attention is focussed on the construction of reduced-order models, which approximate the original system well in a Hankel-norm sense. By applying the slack matrix approach, a delay-dependent sufficient condition is proposed for the robustly asymptotic stability with a Hankel-norm error performance for the error system. Then, the HNMA problem is solved by using the projection approach, which casts the model approximation into a sequential minimisation problem subject to linear matrix inequality constraints by employing the cone complementary linearisation algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods.

Keywords:

• Hankel-norm
• linear matrix inequality
• linear parameter-varying systems
• model approximation
• model reduction
• parameter-varying delay

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 60804002 and 60834003, 973 Project (2009CB320600).