LEADER 04398nam 22005895 450 001 9911018660703321 005 20250806172037.0 010 $a9783031762468$b(electronic bk.) 010 $z9783031762451 024 7 $a10.1007/978-3-031-76246-8 035 $a(MiAaPQ)EBC32256988 035 $a(Au-PeEL)EBL32256988 035 $a(CKB)40150648800041 035 $a(DE-He213)978-3-031-76246-8 035 $a(EXLCZ)9940150648800041 100 $a20250806d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeneralized Homogeneity in Systems and Control Volume I $eFinite-Dimensional Systems /$fby Andrey Polyakov 205 $a2nd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (1282 pages) 225 1 $aCommunications and Control Engineering,$x2197-7119 311 08$aPrint version: Polyakov, Andrey Generalized Homogeneity in Systems and Control Volume I Cham : Springer,c2025 9783031762451 327 $aChapter 1. Introduction -- Chapter 2. Finite-Dimensional Dynamical Systems -- Chapter 3. Stability and Robustness -- Chapter 4. Method of Lyapunov Function -- Chapter 5. Linear Dilation in Euclidean Space -- Chapter 6. Finite-dimensional Homogeneous Mappings -- Chapter 7. Analysis of Homogeneous Systems -- Chapter 8. Discretization of Homogeneous Systems -- Chapter 9. Homogeneous Stabilization of Linear Plant -- Chapter 10. Digitization of Homogeneous Control -- Chapter 11. Upgrading Linear Controller to Homogeneous Feedback -- Chapter 12. Safety-Critical Homogeneous Systems -- Chapter 13. Homogeneous Optimal Control -- Chapter 14. Homogeneous State Estimation -- Chapter 15. Homogeneous Control of Nonlinear Plants -- Chapter 16. Homogeneous Artificial Neural Network -- Chapter 17. Homogeneity in Multi-Agent Systems -- Appendix. 330 $aThis book is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problems. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization. The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in this book) and infinite-dimensional systems (in Volume II). The results are better systematized and easier for readers to study and assimilate. The first volume details the concepts of finite-time and fixed-time stability. Key features of the book include: mathematical models of dynamical systems in finite-dimensional spaces; the theory of linear dilations in Euclidean spaces; homogeneous control and estimation; extensively expanded and original chapters with entirely new treatments of digitization, safety-critical systems, neural networks, and multiagent control; simple methods for an upgrade of existing linear control laws; numerical schemes for a consistent digital implementation of homogeneous algorithms; and experimental results that confirm an improvement of PID controllers. Illustrative examples?numerical results, computer simulations, and real experiments?support all the theoretical material. The coverage of finite-dimensional systems presented in this book is of interest to graduate students of control theory from engineering and applied-mathematical backgrounds and to practising control engineers. 410 0$aCommunications and Control Engineering,$x2197-7119 606 $aAutomatic control 606 $aSystem theory 606 $aControl theory 606 $aEngineering mathematics 606 $aControl and Systems Theory 606 $aSystems Theory, Control 606 $aEngineering Mathematics 615 0$aAutomatic control. 615 0$aSystem theory. 615 0$aControl theory. 615 0$aEngineering mathematics. 615 14$aControl and Systems Theory. 615 24$aSystems Theory, Control. 615 24$aEngineering Mathematics. 676 $a629.8 700 $aPolyakov$b Andrey$0721255 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911018660703321 996 $aGeneralized Homogeneity in Systems and Control Volume I$94414903 997 $aUNINA