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

2004; Elsevier BV; Volume: 54; Issue: 2 Linguagem: Inglês

10.1016/j.sysconle.2004.07.002

1872-7956

Eugênio B. Castelan, Vilemar Gomes da Silva,

Adaptive Control of Nonlinear Systems

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.