Design and Analysis of Control Systems

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