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**Relaxations of parameterized LMIs with control applications.**
*(English)*
Zbl 0919.93028

Parameterized linear matrix inequalities (PLMI) are LMIs whose coefficients are functions of a parameter. LMIs are powerful tools in the analysis and synthesis of robust control problems. Unfortunately, parameterized LMIs are very hard to solve. In contrast, LMIs consist of convex constraints and can be solved by very efficient convex optimization interior-point methods with worst-case polynomial complexity. They offer more freedom and potential than the usual Riccati and Lyapunov tools and provide additional flexibility in control applications.

This paper deals with some effective relaxation techniques to replace PLMIs by a finite set of LMIs. The techniques and tools presented here are applied to Lyapunov-based stability and performance robustness analysis and to linear parameter-varying control. Illustrative examples are given. It is mentioned that the methods are also applicable to \(\mu\)-analysis.

This paper deals with some effective relaxation techniques to replace PLMIs by a finite set of LMIs. The techniques and tools presented here are applied to Lyapunov-based stability and performance robustness analysis and to linear parameter-varying control. Illustrative examples are given. It is mentioned that the methods are also applicable to \(\mu\)-analysis.

Reviewer: W.H.Schmidt (Greifswald)

### MSC:

93B40 | Computational methods in systems theory (MSC2010) |

93B35 | Sensitivity (robustness) |

15A39 | Linear inequalities of matrices |

### Keywords:

parameterized linear matrix inequalities; convex optimization; relaxation; stability; performance robustness; linear parameter-varying control; \(\mu\)-analysis### Software:

LMI toolbox
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\textit{H. D. Tuan} and \textit{P. Apkarian}, Int. J. Robust Nonlinear Control 9, No. 2, 59--84 (1999; Zbl 0919.93028)

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### References:

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