Preface

Robust Control of Uncertain Dynamic Systems has been an active area of research in the last two decades within the control systems community. During the 1980s and 1990s, it even occupied a central role among many areas of control systems research with impressive and significant contributions from many researchers. It has reached a stage of maturity with many universities now offering graduatelevel courses in robust control, resulting in authorship of many textbooks from various viewpoints. Essentially, these research results can be broadly categorized as frequency domain transfer function based results and time domain state space based results. Majority of the textbooks in the current literature focus on topics such as synthesis, H1 control, LQG/LTR, mixed H2=H1 theory, quantitative feedback theory, polynomial methods (inspired by Kharitonov theorem), and quadratic stability. Textbooks that emphasize methods specifically addressing real parameter variations as the modeling error have been relatively scarce. This book intends to fill that gap. This book thus emphasizes time domain state space methods with uncertainty characterized as real parameter variations. It is intended as a textbook for first-year graduate-level students in the area of multivariable robust control. This book is an outgrowth of my sustained interest and contributions to the robust control field which resulted in the coeditorship of an IEEE monograph (with an esteemed colleague and mentor late Prof. Peter Dorato) as well as a short course given in IEEE CDC in 1992 (with another respected senior colleague and friend Prof. George Leitmann). Over the years, the class notes prepared for a series of courses on robust control offered at the Ohio State University helped pave the way for embarking on this task of preparing a textbook on this subject. The prerequisite for understanding the material covered in this book is some basic knowledge of linear control systems, especially linear state space theory and good background of some fundamental matrix theory. The material covered in this book is suitable for a one-semester course or a two-quarter course sequence. Some selected topics from the chapters can be suitable for a single-quarter course. The first chapter, Introduction and Perspective, covers some basic notions of uncertainty characterization and various robustness concepts. The second chapter is one of the main chapters of the book, thoroughly covering the topic of perturbation bounds for robust stability of linear state space models (i.e., stability robustness analysis). Chapter 3 covers the aspect of performance robustness analysis by casting the problem as a robust root clustering (or robust D-stability) problem, thereby