Powers of SPR functions and preservation properties |
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| Institution: | 1. Departamento de Ciencias, Universidad Iberoamericana, Av. Prol. Paseo de la Reforma 880, 01210, Lomas de Santa Fe, Mexico;2. CINVESTAV-IPN Control Automatico, P.O. Box 14-740, D.F. col. facatenco 07300, Mexico;1. Zhongxing Telecommunication Equipment Corporation, Ltd. People''s Republic of China;2. Department of Automation, Shanghai Jiaotong University, Shanghai 200030, People''s Republic of China;1. Applied Statistics Laboratory, General Electric Research, 1 Research Circle, Building K1, Room 4C41A, Niskayuna, NY 12309, USA;2. Department of Biometry and Statistics, School of Public Health, University at Albany, One University Place, Rensselaer, NY 12144-3456, USA;1. Dipartimento di Sistemi e Informatica, Universitá di Firenze, Via di S. Marta, 3-50139 Firenze, Italy;1. HEUDIASYC (UMR CNRS 6599), Centre de Recherche de Royallieu, Université de Technologie de Compiègne, BP 20529, 60205 Compiègne, France;2. Department of Mechanical Engineering, Massachussets Institute of Technology, Cambridge, MA 02139-4307, USA;1. Bell Laboratories, Lucent Technologies Room 2C-525, 700 Mountain Avenue, Murray Hill, NJ 07974-0636, USA;2. Institut für Mathematik, Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany |
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| Abstract: | Basic properties of a new class of strictly positive real (SPR) functions are stated. Four problems are studied. The first deals with SPR preservation of transfer functions, obtained under the composition of polynomials with SPR0 functions. The second deals with Hurwitz stability preservation of the numerator of transfer functions, obtained under the composition of polynomials with SPR0 functions. The third deals with making a Hurwitz closed-loop plant, an SPR0 function by substituting s by SPR0 functions. The four deals with the synthesis of simultaneous SPR feedback plants. For the new class of SPR0 functions, a characterization is presented. For the first and second problems, sufficient conditions are presented using the new class of SPR0 functions. For the third and four problems, two examples are presented, the first being for simultaneous SPR closed-loop systems via constant controllers. The second is for simultaneous stabilization via universal feedback adaptive control. |
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