Linear Matrix Inequality Method for a Quadratic Performance Index Minimization Problem with a class of Bilinear Matrix Inequality Conditions

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Tanemura, M.^1 ; Chida, Y.^2

Interdisciplinary Graduate School of Science and Technology, Shinshu University, Japan^1

Faculty of Engineering, Shinshu University, Japan^2

关键词: Bilinear matrix inequality;    Convex minimization;    Linear matrix inequality method;    Minimization problems;    Performance indices;    Quadratic performance indices;    State feedback gain;    Switched system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012047/pdf
DOI  :  10.1088/1742-6596/744/1/012047

来源: IOP

【 摘 要 】

There are a lot of design problems of control system which are expressed as a performance index minimization under BMI conditions. However, a minimization problem expressed as LMIs can be easily solved because of the convex property of LMIs. Therefore, many researchers have been studying transforming a variety of control design problems into convex minimization problems expressed as LMIs. This paper proposes an LMI method for a quadratic performance index minimization problem with a class of BMI conditions. The minimization problem treated in this paper includes design problems of state-feedback gain for switched system and so on. The effectiveness of the proposed method is verified through a state-feedback gain design for switched systems and a numerical simulation using the designed feedback gains.