On the solution of a Sylvester equation appearing in descriptor systems control theory

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• 作者：Castelan ; Eugê ; nio B. ; da Silva ; Vilemar Gomes
• 关键词：Descriptor systems ; Minimal-order observers ; Output feedback ; Sylvester equation ; Eigenstructure assignment ; Regional pole-placement
• 刊名：Systems & Control Letters
• 出版年：2005
• 出版时间：February, 2005
• 年：2005
• 卷：54
• 期：2
• 页码：109-117
• 全文大小：220 K

文摘

The solution of a generalized Sylvester equation associated to a linear descriptor system and subject to some rank and regional pole-placement constraints, is studied in this paper. Under the hypothesis of strong-detectability of the descriptor system, a sequence of coordinate transformations is proposed such that the considered problem can be solved through a Sylvester equation associated to a detectable reduced-order normal system. Thus, solutions to this equation can be found either by eigenstructure assignment or by regional pole-placement in LMI-type regions of the complex plane. The proposed results are motivated from its use for designing minimal-order observers and for computing output feedback control laws by a particular technique. Some numerical results are reported and possible extensions for the proposed approach are commented.