at Google ScholarTitle data
Mironchenko, Andrii:
Input-to-State Stability : Theory and Applications.
Cham, Switzerland
:
Springer
,
2023
. -
XVI, 406 p.
- (Communications and Control Engineering Series
)
ISBN 978-3-031-14674-9
| Review: |
DOI: https://doi.org/10.1007/978-3-031-14674-9
Abstract in another language
”Input-to-State Stability” presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems.
The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs).
Features of the book include:
• a comprehensive overview of the theoretical basis of ISS;
• a description of the central applications of ISS in nonlinear control theory;
• a detailed discussion of the role ofsmall-gain methods in the stability of nonlinear networks; and
• an in-depth comparison of ISS for finite- and infinite-dimensional systems.
The book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS.
Further data
| Item Type: | Book / Monograph |
|---|---|
| Additional notes: | Contents:
1 Ordinary Differential Equations with Measurable Inputs 1.1 Ordinary Differential Equations with Inputs 1.2 Existence and Uniqueness Theory 1.3 Boundedness of Reachability Sets 1.4 Regularity of the Flow 1.5 Uniform Crossing Times 1.6 Lipschitz and Absolutely Continuous Functions 1.7 Spaces of Measurable and Integrable Functions 1.8 Concluding Remarks 1.9 Exercises References 2 Input-to-State Stability 2.1 Basic Definitions and Results 2.2 ISS Lyapunov Functions 2.3 Local Input-to-State Stability 2.4 Asymptotic Properties for Control Systems 2.5 ISS Superposition Theorems 2.6 Converse ISS Lyapunov Theorem 2.7 ISS, Exponential ISS, and Nonlinear Changes of Coordinates 2.8 Integral Characterization of ISS 2.9 Semiglobal Input-to-State Stability 2.10 Input-to-State Stable Monotone Control Systems 2.11 Input-to-State Stability, Dissipativity, and Passivity 2.12 ISS and Regularity of the Right-Hand Side 2.13 Concluding Remarks 2.14 Exercises References 3 Networks of Input-to-State Stable Systems 3.1 Interconnections and Gain Operators 3.2 Small-Gain Theorem for Input-to-State Stability of Networks 3.3 Cascade Interconnections 3.4 Example: Global Stabilization of a Rigid Body 3.5 Lyapunov-Based Small-Gain Theorems 3.6 Tightness of Small-Gain Conditions 3.7 Concluding Remarks 3.8 Exercises References 4 Integral Input-to-State Stability 4.1 Basic Properties of Integrally ISS Systems 4.2 iISS Lyapunov Functions 4.3 Characterization of 0-GAS Property 4.4 Lyapunov-Based Characterizations of iISS Property 4.5 Example: A Robotic Manipulator 4.6 Integral ISS Superposition Theorems 4.7 Integral ISS Versus ISS 4.8 Strong Integral Input-to-State Stability 4.9 Cascade Interconnections Revisited 4.10 Relationships Between ISS-Like Notions 4.11 Bilinear Systems 4.12 Small-Gain Theorems for Couplings of Strongly iISS Systems 4.13 Concluding Remarks 4.14 Exercises References 5 Robust Nonlinear Control and Observation 5.1 Input-to-state Stabilization 5.2 ISS Feedback Redesign 5.3 ISS Control Lyapunov Functions 5.4 ISS Backstepping 5.5 Global Stabilization of Axial Compressor Model. Gain Assignment Technique 5.6 Event-based Control 5.7 Outputs and Output Feedback 5.8 Robust Nonlinear Observers 5.9 Observers and Dynamic Feedback for Linear Systems 5.10 Observers for Nonlinear Systems 5.11 Concluding Remarks and Extensions 5.12 Exercises References 6 Input-to-State Stability of Infinite Networks 6.1 General Control Systems 6.2 Infinite Networks of ODE Systems 6.3 Input-to-State Stability 6.4 ISS Superposition Theorems 6.5 ISS Lyapunov Functions 6.6 Small-Gain Theorem for Infinite Networks 6.7 Examples 6.8 Concluding Remarks 6.9 Exercises References 7 Conclusion and Outlook 7.1 Brief Overview of Infinite-Dimensional ISS Theory 7.2 Input-to-State Stability of Other Classes of Systems 7.3 ISS-Like Stability Notions References Appendix A: Comparison Functions and Comparison Principles Appendix B: Stability Appendix C: Nonlinear Monotone Discrete-Time Systems Index |
| Keywords: | input-to-state stability; nonlinear systems; Lyapunov functions; small-gain theorem; large-scale networks; robust stability; discrete-time systems; monotone systems; infinite networks; robust control; nonlinear control; comparison functions |
| Subject classification: | Mathematics Subject Classification Code: 93-02 (93D25 93C10 93D30 93C15 93C20) |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields > Advanced Fields > Nonlinear Dynamics |
| Result of work at the UBT: | No |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 06 Mar 2025 08:38 |
| Last Modified: | 06 Mar 2025 08:38 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92631 |