On the design of observers for generalized state space systems using singular value decomposition |
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| Authors: | MOHAMMAD EL-TOHAMI V. LOVASS-NAGY R. MUKUNDAN |
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| Affiliation: | 1. Department of Mathematics , Clarkson College of Technology , Potsdam, New York, 13676, U.S.A.;2. Department of Mathematics , Military Technical College , Kobry El-Kobba, Cairo, Egypt;3. Department of Electrical and Computer Engineering , Clarkson College of Technology , Potsdam, New York, 13676, U.S.A.;4. Department of Electrical and Computer Engineering , Clarkson College of Technology , Potsdam, New York, 13676, U.S.A. |
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| Abstract: | In this paper a method is developed for the design of Luenberger-type observers for linear time-invariant control systems whose state equation is of the form Ex= Ax+ Bu where E is a singular square matrix. The method is based on the singular-value decomposition of the matrix E, and on the reduction of the equation Ex= Ax +Bu to a system consisting of a differential equation of the form w1, = F1w1 + F2 + w2 +G1u and an algebraic equation of the form H1w1 +H2w2 + G1u = 0. If w2 can be eliminated from the differential equation by the aid of the algebraic equation and the original output equation of the system, the method yields a reduced-order observer for the generalized state space system. |
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