作者： R.E. Mahony , U. Helmke
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摘要: Journal of Mathematical Systems, Estimation, and Controlc1995 Birkhauser-BostonVol. 5, No. 2, 1995, pp. 1{32SystemAssignmentandPolePlacemenforSymmetricRealisationsR.E.MahonyyU.HelmkeAbstractIn this pap er we consider the problem system assignment forthe class linear output feedback systems having symmetric statespacerealisations.Forsuchsystemstheclassicalp oleplacementtask can b e considered as a degenerate case more general sys-tem problem.It is shown that state spacerealisation assigned arbitrary (real) p oles via feedbackifandonlythereareatleastasmanysysteminputsstates.The task computing gains for ap-proachedbyderivinggradientowswhichminimizesuitableleastsquares distance functions on smo oth manifolds feedbackequivalentrealisations.Theseordinarydi erentialequationspro-vide insightintothecomplex structureofsystems assignmenand ole placement problems.Computing limiting values theows provides metho d determining optimal (p placement) even when exactsolutions to do es not exist.The ds are also gen-eralised simultaneous multiple problem.Keywords:outputfeedbacksystemassignment,p oleplacemensymmetricsystemsAMS Sub ject Classi cations:93A30, 93B55, 34C40Received Decemb 22, 1993; received in nal form Septemb 12, 1994.Summaryapp eared Volume Numb 1995.yThe authors wish acknowledge funding activities Co op erativeResearch Centre Robust Adaptive Systems by Australian CommonwealthGovernment under erative Research Centres Program supp ort GrantI-0184-078.06/91 from G.I.F., German-Israeli Foundation Scienti c Researchand Development.1