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 Lyapunovs 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.
1. Introduction and Motivation
1.1. Willems behavioral framework for system modeling
1.2. Notions of stability and stabilizability
1.3. Three cases in consideration
2. Blending feedback laws
2.1. The Backstepping design
2.2. Hybrid dynamical systems
2.3. Blending a backstepping controller with a local stabilizer
2.4. Concepts of optimal control
2.5. Blending a global optimal controller with a local prescribed controller
3. Blending stability concepts
3.1. Almost everywhere asymptotic stability
3.2. Input-to-state stability
3.3. Application to the analysis of interconnected systems
A. Related mathematical concepts
a. Basic concepts and results of measure theory
b. Basic concepts and results of integration and differentiation
c. Basic results of existence and uniqueness of solutions of ODEs
d. The Perron-Frobenius and Koopman operators
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. ls$
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