H_∞ and H₂ stabilisers via static output feedback based on coordinate transformations with free variables

Abstract

This article designs H _∞ and H ₂ stabilisers, respectively, for linear time-invariant systems via static output feedback (SOF). A state coordinate transformation of controlled system generates a dummy system with lower dimension, which cannot be directly influenced by the SOF stabiliser. Then the H _∞ (H ₂) stabiliser via SOF may be obtained by solving proper linear matrix inequality (LMI). This LMI is feasible only if the dummy system has a state feedback stabiliser with the same H _∞ (H ₂) index. Meanwhile, a free matrix variable in coordinate transformation can act as the state feedback gain matrix. Hence after the design of dummy system, the SOF stabiliser can be determined if certain LMI is feasible. This method does not concern any conservative reduction or enlargement of matrix inequalities. Numerical examples show the validity of the proposed algorithms.

Keywords:

• H ₂
• static output feedback
• coordinates transformation
• LMI
• optimal control
• H _∞ control

Acknowledgement

This article was supported by National Natural Science Foundations of China (60674021). The authors would like to thank all the anonymous reviewers for their helpful comments.