Eigenstructure Assignment for Linear Time-Varying Systems: a Differential Sylvester Equation Approach

미분 Sylvester 방정식을 이용한 선형 시변 시스템의 고유구조 지정기법

  • 최재원 (부산대학교 기계공학부 및 기계기술연구소) ;
  • 이호철 (부산대학교 기계공학부)
  • Published : 1999.10.01

Abstract

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

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