Linear Systems and Optimal Control

1. Front Matter

   Pages I-VIII

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2. State-Space Descriptions

   • Charles K. Chui, Guanrong Chen

   Pages 1-7

3. State Transition Equations and Matrices

   • Charles K. Chui, Guanrong Chen

   Pages 8-15

4. Controllability

   • Charles K. Chui, Guanrong Chen

   Pages 16-25

5. Observability and Dual Systems

   • Charles K. Chui, Guanrong Chen

   Pages 26-35

6. Time-Invariant Linear Systems

   • Charles K. Chui, Guanrong Chen

   Pages 36-48

7. Stability

   • Charles K. Chui, Guanrong Chen

   Pages 49-69

8. Optimal Control Problems and Variational Methods

   • Charles K. Chui, Guanrong Chen

   Pages 70-80

9. Dynamic Programming

   • Charles K. Chui, Guanrong Chen

   Pages 81-93

10. Minimum-Time Optimal Control Problems

    • Charles K. Chui, Guanrong Chen

    Pages 94-105

11. Notes and References

    • Charles K. Chui, Guanrong Chen

    Pages 106-118

12. Back Matter

    Pages 119-155

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A knowledge of linear systems provides a firm foundation for the study of optimal control theory and many areas of system theory and signal processing. State-space techniques developed since the early sixties have been proved to be very effective. The main objective of this book is to present a brief and somewhat complete investigation on the theory of linear systems, with emphasis on these techniques, in both continuous-time and discrete-time settings, and to demonstrate an application to the study of elementary (linear and nonlinear) optimal control theory. An essential feature of the state-space approach is that both time-varying and time-invariant systems are treated systematically. When time-varying systems are considered, another important subject that depends very much on the state-space formulation is perhaps real-time filtering, prediction, and smoothing via the Kalman filter. This subject is treated in our monograph entitled "Kalman Filtering with Real-Time Applications" published in this Springer Series in Information Sciences (Volume 17). For time-invariant systems, the recent frequency domain approaches using the techniques of Adamjan, Arov, and Krein (also known as AAK), balanced realization, and oo H theory via Nevanlinna-Pick interpolation seem very promising, and this will be studied in our forthcoming monograph entitled "Mathematical Ap­ proach to Signal Processing and System Theory". The present elementary treatise on linear system theory should provide enough engineering and mathe­ of these two subjects.

• Nonlinear system
• Notation
• optimal control
• programming
• system
• systems engineering
• complexity

• Department of Mathematics and Department of Electrical Engineering, Texas A & M University, College Station, USA

  Charles K. Chui

• Department of Electrical and Computer Engineering, Rice University, Houston, USA

  Guanrong Chen

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