Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions  

作　　者：Pan Xiong Feng Wang Xibin Cao Guangren Duan 

机构地区：[1]School of Astronautics,Harbin Institute of Technology [2]National and Local United Research Center of Small Satellite Technology

出　　处：《Journal of Systems Engineering and Electronics》2013年第6期984-991,共8页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China (60904051;61021002)

摘　　要：The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

关 键 词：linear uncertain system robust D-stability analysis linear matrix inequality （LMI） condition affine parameterdependent Lyapunov function matrix polytope. 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TP271[自动化与计算机技术—控制科学与工程]