LEADER 04815nam 22006975 450 001 9910299837703321 005 20200705150440.0 010 $a3-319-15717-5 024 7 $a10.1007/978-3-319-15717-7 035 $a(CKB)3710000000394684 035 $a(EBL)2095428 035 $a(SSID)ssj0001501158 035 $a(PQKBManifestationID)11771909 035 $a(PQKBTitleCode)TC0001501158 035 $a(PQKBWorkID)11524120 035 $a(PQKB)10648959 035 $a(DE-He213)978-3-319-15717-7 035 $a(MiAaPQ)EBC2095428 035 $z(PPN)258862033 035 $a(PPN)185486878 035 $a(EXLCZ)993710000000394684 100 $a20150408d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays /$fby Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (145 p.) 225 1 $aSpringerBriefs in Control, Automation and Robotics,$x2192-6786 300 $aDescription based upon print version of record. 311 $a3-319-15716-7 320 $aIncludes bibliographical references and index. 327 $aIntroduction to the Stability of Time-Delay Systems -- Introduction to Analytic Curves -- Analytic Curve Perspective for Time-Delay Systems -- Computing Puiseux Series for a Critical Pair -- Invariance Property: A Unique Idea for Complete Stability Analysis -- Invariance Property for Critical Imaginary Roots (CIRs) with Index g = 1 -- Invariance Property for Critical Imaginary Roots with Index n = 1 -- Invariance Conjecture and Frequency-Sweeping Framework -- Complex Stability for Time-Delay Systems: A Unified Approach -- Extension to Neutral Time-Delay Systems -- Concluding Remarks and Further Perspectives. 330 $aIn this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensurate delays. The text describes an analytic curve perspective which allows a deeper understanding of spectral properties focusing on the asymptotic behavior of the characteristic roots located on the imaginary axis as well as on properties invariant with respect to the delay parameters. This asymptotic behavior is shown to be related by another novel concept, the dual Puiseux series which helps make frequency-sweeping curves useful in the study of general time-delay systems. The comparison of Puiseux and dual Puiseux series leads to three important results: an explicit function of the number of unstable roots simplifying analysis and design of time-delay systems so that to some degree they may be dealt with as finite-dimensional systems; categorization of all time-delay systems into three types according to their ultimate stability properties; and a simple frequency-sweeping criterion allowing asymptotic behavior analysis of critical imaginary roots for all positive critical delays by observation. Academic researchers and graduate students interested in time-delay systems and practitioners working in a variety of fields ? engineering, economics and the life sciences involving transfer of materials, energy or information which are inherently non-instantaneous, will find the results presented here useful in tackling some of the complicated problems posed by delays. 410 0$aSpringerBriefs in Control, Automation and Robotics,$x2192-6786 606 $aControl engineering 606 $aSystem theory 606 $aElectrical engineering 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aCommunications Engineering, Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/T24035 615 0$aControl engineering. 615 0$aSystem theory. 615 0$aElectrical engineering. 615 14$aControl and Systems Theory. 615 24$aSystems Theory, Control. 615 24$aCommunications Engineering, Networks. 676 $a519 676 $a620 676 $a621.382 676 $a629.8 700 $aLi$b Xu-Guang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720882 702 $aNiculescu$b Silviu-Iulian$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aCela$b Arben$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299837703321 996 $aAnalytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays$92521963 997 $aUNINA