Optimal and Robust Control

Luigi Fortuna is a Full Professor of System Theory with the Università degli Studi di Catania, Catania, Italy. He has published more than 600 scientific papers regarding robust control, nonlinear science and complexity, chaos, cellular neural networks, softcomputing strategies for control and robotics, micronanosensor and smart devices for control, and nanocellular neural networks modeling.Mattia Frasca is presently as Associate Professor at the University of Catania, Italy and teaches Process Control and Complex Adaptive Systems. His scientific interests include linear systems, nonlinear dynamics, analysis and control of complex systems, and bio-inspired robotics.Arturo Buscarino is currently a researcher in Automatic Control at the University of Catania, Italy. He is IEEE Senior Member. His scientific interests include nonlinear circuits and systems, chaos and synchronization, memristors, fuzzy logic, control systems, Cellular Nonlinear Networks, and plasma engineering.

• 1. Modelling of Uncertain Systems and the Robust Control Problem. 2. Fundamentals of Stability. 3. Kalman Canonical Decomposition. 4. Singular Value Decomposition. 5. Open-loop Balanced Realization. 6. Reduced Order Models and Symmetric Systems. 7. Variational Calculus and Linear Quadratic Optimal Control. 8. Closed-loop Balanced Realization. 9. Positive-real, Bounded-real, and Negative-imaginary Systems. 10. Enforcing the Positive-real or the Negative-imaginary Property in a Linear Model. 11. H∞ linear control. 12. Linear Matrix Inequalities for Optimal and Robust Control. 13. The Class of Stabilizing Controllers. 14. Formulation and Solution of Matrix Algebraic Problems Through Optimization Problems. 15. Time-delay Systems. Appendix A. Norms. Appendix B. Algebraic Riccati Equations. Appendix C. Invariance under Frequency Transformations.