Proceedings of the KIEE Conference (대한전기학회:학술대회논문집)

The Korean Institute of Electrical Engineers (대한전기학회)
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Mixed $L_1/H_{\infty}$ Suboptimal Control: A LMI Approach

LMI를 이용한 $L_1/H_{\infty}$ 준최적 제어기법

  • Chun, K.H. (School of Electrical Engineering) ;
  • Noh, D.J. (School of Electrical Engineering) ;
  • Seo, J.H. (School of Electrical Engineering)
  • 천관호 (서울대학교 전기공학부) ;
  • 노대종 (서울대학교 전기공학부) ;
  • 서진헌 (서울대학교 전기공학부)
  • Published : 1996.07.22
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Abstract

In this paper, we consider the mixed $L_1/H_{\infty}$ problems of finding internally stabilizing controllers which minimize the peak-to-peak gain of a certain closed loop transfer function with $H_{\infty}$-norm constraint on other closed loop transfer function(or vise versa). This problem is a useful framework for designing a controller with the norm constraints upon time and frequency domain. We formulate the mixed $L_1/H_{\infty}$ problem as LMI problems by using the reachable set. This paper offers the sufficient condition for the existence of suboptimal state feedback controller, and shows that suboptimal solution can be obtained by solving a finite-dimensional convex optimization and a line search.

Keywords