VI 5.3 Proof of the measurement-feedback result. 144 5.4 Relaxation of the a priori assumptions .. 165 5.4.1 Including the feedthroughs . . . . . 165 5.4.2 How to 'remove' the regularity assumptions 174 6 Examples and conclusions 177 6.1 Delay systems in state-space . . . . . . . . . . 177 6.1.1 Dynamic controllers for delay systems. 180 184 6.1.2 A linear quadratic control problem . . 6.1.3 Duality ............... . . 189 6.2 The mixed-sensitivity problem for delay systems 192 6.2.1 Introduction and statement of the problem. 192 6.2.2 Main result .............. . 194 6.3 Conclusions and directions for future research. 200 A Stability theory 205 A.1 205 A.2 206 B Differentiability and some convergence results 207 B.l 207 208 B.2 B.3 209 209 B.4 B.5 209 B.6 211 B.7 213 214 C The invariant zeros condition C.1 214 221 D The relation between P, Q and P 221 D.1 ............ .... . Bibliography 230 239 Index Preface Control of distributed parameter systems is a fascinating and challenging top ic, from both a mathematical and an applications point of view. The same can be said about Hoc-control theory, which has become very popular lately. I am therefore pleased to present in this book a complete treatment of the state-space solution to the Hoo-control problem for a large class of distributed parameter systems.

This book presents new computational tools for the H? control of distributed parameter systems in which transfer functions are considered as input-output descriptions for the plants to be controlled. The emphasis is on the computation of the controller parameters and reliable implementation. The authors present recent studies showing that the simplified skew-Toeplitz method is applicable to a wide class of systems, supply detailed examples from systems with time delays and various engineering applications, and discuss reliable implementation of the controller, complemented by a software based on MATLAB. Frequency Domain Techniques for H? Control of Distributed Parameter Systems is intended for advanced undergraduate and early graduate students interested in robust control of distributed parameter systems?time delay systems?as well as researchers and engineers working in related fields. It can be used in the following courses: Introduction to Robust Control with Applications to Distributed Parameter Systems and Introduction to Robust Control with Applications to Time Delay Systems.

This report describes progress in the development and application of H-infinity-optimal control theory to distributed parameter systems. This research is intended to develop both theory and algorithms capable of providing realistic control systems for physical plants which are appropriately modeled as infinite dimensional linear systems, such as large space structures. In pursuing this program, we have focused on issues motivated by specific models of infinite dimensional systems. Our main results are as follows: We have extended outer factor absorption results to cover certain irrational outer factors. This is in order to justify transformations used in a step for further explicit solution. We have generalized previous results on the single-input/single-output (SISO) mixed sensitivity problem to the case of irrational outer factor and unstable plant. We have solved a multi-input/output mixed sensitivity problem which cannot be treated by previous results. Finally, we developed a technique for numerically computing the optimal value of weighted mixed sensitivity for SISO systems, for the case where explicit symbolic inner/outer factorizations are not possible.

The applications of the theory of Optimal Control of distributed parameters is an extremely wide field and, although a large number of questions remain open, the whole subject continues to expand very rapidly. The author does not attempt to cover the field but does discuss a number of the more interesting areas of application.

Research in control and estimation of distributed parameter systems encompasses a wide range of applications including both fundamental science and emerging technologies. The latter include smart materials (piezoceramics, shape memory alloys, magnetostrictives, electrorheological fluids) fabrication and testing, design of high-pressure chemical vapor deposition (CVD) reactors for production of microelectronic surfaces (e.g., semiconductors), while the former include groundwater contamination cleanup and other environmental modeling questions, climatology, flow control, and fluid-structure interactions as well as more traditional topics in biology, mechanics, and acoustics. These expository papers provide substantial stimulus to both young researchers and experienced investigators in control theory. Includes a comprehensive and lucid presentation that relates frequency domain techniques to state-space or time domain approaches for infinite-dimensional systems including design of robust stabilizing and finite-dimensional controllers for infinite-dimensional systems. It focuses on these two approaches to control design in an integrated system theoretic framework. This is excellent reading for researchers in both the frequency domain and time domain control communities. In other articles, topics considered include pointwise control of distributed parameter systems, bounded and unbounded sensors and actuators, stabilization issues for large flexible structures, and an overview discussion of damping models for flexible structures.