Stability and robustness analysis of MIMO MRAC using K_p=L₂D₂S₂ factorization

Abstract

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of K_p = L ₂ D ₂ S ₂ factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the L_p and L _2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.

Keywords:

• MIMO systems
• Unmodeled dynamics
• K _p = L ₂ D ₂ S ₂ factorization
• MRAC

Acknowledgments

The authors would like to thank the reviewers for their comments and suggestions. This work is supported by Program for New Century Excellent Talents in Universities of China (NCET-05-0607), National Natural Science Foundation of China (60774010), and Project for Fundamental Research of Natural Sciences in Universities of Jiangsu Province (07KJB510114).