Modern Control System Theory and Design, 2nd Edition

8.11.  AN INTRODUCTION TO H^∞ CONTROL CONCEPTS [16, 17]

In the presentation of this book, the classical frequency-domain approach and the modern state-variable time-domain approach have been presented in parallel. It has been shown that they complement each other. Prior to the 1960s, the frequency-domain approach predominated. With the advent of the space race, the availability of practical digital computers, modem optimal control theory, and the state-variable approach in the early 1960s, the pendulum swung to the time-domain approach. The 1960s and 1970s saw an abundant amount of work performed on applying modern optimal control theory, which is presented in Chapter 11 in this book. In the early 1980s, a new technique has emerged known as H^∞ control theory which combines both the fequency- and time-domain approaches to provide a unified answer. Zames is given credit for its introduction with his paper in the IEEE Transactions on Automatic Control [16]. The H^∞ approach has dominated the trend of control-system development in the 1980s and 1990s. A complete treatment of the subject of H^∞ is complex, and beyond the scope of this book. However, we can expand the concepts of robustness (introduced in Section 8.10) and sensitivity (introduced in Chapter 5), together with the frequency and state-variable domain techniques presented in this book to introduce the basic concepts of H^∞ control theory and apply it to some simple problems. This is the objective of this and the following sections. ...