广义系统混合h2h∞性能的可靠控制器设计.pdfVIP

Vol. 31, No. 2 ACTA AUTOMATICA SINICA March, 2005 Reliable Controller Design with Mixed H2/H∞ Performance for Descriptor Systems1) CHEN Yue-Peng ZHANG Qing-Ling ZHAI Ding (Institute of Systems Science, Northeastern University, Liaoning, Shenyang 110004) (E-mail: chenyuepeng@) Abstract The design problem of a reliable observer-based controller with mixed H2/H∞ perfor- mance for descriptor systems is discussed using linear matrix inequality (LMI) approach. First, the design problems of H2 and H∞ controllers are discussed, respectively. Secondly, when there are partial actuator faults for the descriptor system, controllers with H2 and H∞ performance are de- signed, respectively. Finally, a numerical example is given to illustrate the design procedures and their e?ectiveness. Key words Descriptor systems, mixed H2/H∞ performance, reliable controller, linear matrix inequality 1 Introduction H2 optimal control for linear systems possesses many excellent properties except robustness. H∞ control can overcome robust problems of system, yet it sacri?ces other properties[1]. Therefore, Berstein [2] et al. put forward the design idea of mixed H2/H∞ control. The approach has received extensive attention and made much progress[3] since it can better resolve the problem of robust performance and performance index. In recent years, there have been great interests in design reliable controllers for linear systems. Using algebraic Riccati equation, Veillette[4] has brought forward the design method to reliable con- [5] trollers with H∞ performance. Veillette has also devised a class of reliable linear quadratic (LQ) controllers. In some cases, many other performances are sacri?ced fo