H∞-Control for Distributed Parameter Systems: A State-Space Approach

1. Front Matter

   Pages i-vii

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2. Introduction

   • Bert van Keulen

   Pages 1-16

3. Pritchard-Salamon systems

   • Bert van Keulen

   Pages 17-74

4. Linear quadratic control and frequency domain inequalities

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   Pages 75-100

5. H _∞-control with state-feedback

   • Bert van Keulen

   Pages 101-129

6. H _∞-control with measurement-feedback

   • Bert van Keulen

   Pages 130-176

7. Examples and conclusions

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   Pages 177-204

8. Stability theory

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   Pages 205-206

9. Differentiability and some convergence results

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   Pages 207-213

10. The invariant zeros condition

    • Bert van Keulen

    Pages 214-220

11. The relation between P, Q and \(\bar{P}\)

    • Bert van Keulen

    Pages 221-229

12. Back Matter

    Pages 230-241

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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.

• Invariant
• Mathematica
• control
• control theory
• duality
• proof
• stability
• stability theory

• Department of Mathematics, University of Groningen, The Netherlands

  Bert Keulen

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