Invariance of characteristic values and L∞ norm under lossless positive real transformations. Issue 9 (June 2016)

• Record Type: Journal Article
• Authors: Buscarino, A.; Fortuna, L.; Frasca, M.; Xibilia, M.G.
• Is Part Of: Journal of the Franklin Institute. Volume 353:Issue 9(2016:Jun.)
• Page Start: 2057
• Page End: 2073
• Publication Date: 2016-06
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2016.03.019
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: In this paper the invariance of the characteristic values and of the L ∞ norm of linear time-invariant (LTI) systems under lossless positive real transformations is proven. Given a LTI system with transfer function matrix G ( s ), the transformation s ← F ( s ) with F ( s ) being an arbitrary lossless positive real function of order n F is considered, and the algebraic Riccati equations (AREs) allowing to assess some properties of the transformed system G ( F ( s ) ) are investigated. It is proven that, under such transformations, the solutions of the AREs associated to system G ( F ( s ) ) are related to those of G ( s ) . From this property, it derives that G ( F ( s ) ) and G ( s ) have the same L ∞ norm and that the characteristic values of G ( F ( s ) ) are those of G ( s ), each with multiplicity n F .