This book provides methods to unify different approaches to tackle stability theory problems. In particular, it presents a methodo...
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This book provides methods to unify different approaches to tackle stability theory problems. In particular, it presents a methodology to blend approaches obtained from measure theory with methods obtained from Lyapunov's stability theory. The author summarizes recent works on how different analysis/design methods can be unified and employed for systems that do not belong to either of domains of validity.
Provides a framework to blend different approaches for controller design
Presents measure-theoretical techniques for the analysis and design of nonlinear systems
Includes supplementary material: sn.pub/extras
Humberto Stein Shiromoto is a postdoctoral researcher at the Australian Centre for Field Robotics, The University of Sydney, Australia. His research interests include Lyapunov's stability theory and nonlinear hybrid systems with applications to cyber-physical systems and robotics.
Zusammenfassung "In this book, the author addresses some problems regarding the design of feedback laws and an analysis of the interaction of the interconnected systems. ... this is a well-structured book intended for researchers in control theory and engineers familiar with the topic." (Mohamed Ouzahra, Mathematical Reviews, December, 2017)
Inhalt 1. Introduction and Motivation1.1. Willem's behavioral framework for system modeling1.2. Notions of stability and stabilizability1.3. Three cases in consideration2. Blending feedback laws2.1. The Backstepping design2.2. Hybrid dynamical systems2.3. Blending a backstepping controller with a local stabilizer2.4. Concepts of optimal control2.5. Blending a global optimal controller with a local prescribed controller3. Blending stability concepts3.1. Almost everywhere asymptotic stability3.2. Input-to-state stability3.3. Application to the analysis of interconnected systemsA. Related mathematical conceptsa. Basic concepts and results of measure theoryb. Basic concepts and results of integration and differentiationc. Basic results of existence and uniqueness of solutions of ODEsd. The Perron-Frobenius and Koopman operators