This book presents the theoretical foundations of the comparison approach and demonstrates how this method can be used for the development of techniques for the analysis and design of control systems in the state-space domain. It provides a framework for using the comparison approach to solve fundamental analysis and design problems of control systems, including invariance and contractivity, stability analysis and constrained control.

Within this framework, the book shows the reader that the invariance of sets represented by sublevel subsets, the control-invariant regions, the stability properties and the design of constrained controllers for both continuous-time and discrete-time systems can be investigated using comparison systems. The dual approach of analysis and design, based on the representation of state-space regions in terms of a number of generators and a generating function, is developed. Polyhedral invariant sets, polyhedral control invariance, stability analysis using polyhedral Lyapunov functions and constrained control under linear constraints are also investigated.

Comparison Methods in Control begins with an introduction and discusses stability, Lyapunov theory, and representation of connected sets. The book progresses through comparison in different contexts, such as comparison and invariance, comparison and stability, dual comparison systems and control invariance. Constrained regulation problems and constrained control of disturbed and parameter uncertain systems are all given equal attention. Researchers and postgraduate students with backgrounds in systems analysis, control and applied mathematics will find this monograph of interest.

Autorentext

Professor George Bitsoris received his B.Sc. degree in Electrical and Mechanical Engineering from the Technical University of Athens and his Ph.D. degree from the University Paul Sabatier of Toulouse in 1978. He became a professor at the Department of Electrical and Computer Engineering at the University of Patras in 1991 and since 2017 he has been professor emeritus. He has also been a visiting professor at several institutions, including Supélec-Paris and the Polytechnic University of Catalonia. His main areas of research interests are comparison methods, nonlinear systems, stability and constrained control systems.