This volume studies dynamical systems with inputs and outputs. It develops mathematical models, stability theory, and control design for engineered and natural systems.
Part I. Foundations
Chapter 1. System Models
1.1 State-space representation 1.2 Input-output models 1.3 Continuous and discrete systems 1.4 Linear vs nonlinear systems 1.5 Examples
Chapter 2. Linear Systems
2.1 State equations 2.2 Matrix exponential 2.3 Solution of linear systems 2.4 Examples 2.5 Applications
Chapter 3. Signals and Responses
3.1 Impulse response 3.2 Convolution representation 3.3 Transfer functions 3.4 Frequency response 3.5 Examples
Part II. Stability and Control
Chapter 4. Stability Theory
4.1 Definitions of stability 4.2 Lyapunov methods 4.3 Asymptotic stability 4.4 Applications 4.5 Examples
Chapter 5. Controllability and Observability
5.1 Definitions 5.2 Kalman criteria 5.3 Canonical forms 5.4 Applications 5.5 Examples
Chapter 6. Feedback Systems
6.1 Feedback loops 6.2 Closed-loop behavior 6.3 Stability analysis 6.4 Applications 6.5 Examples
Part III. Control Design
Chapter 7. State Feedback
7.1 Pole placement 7.2 Stabilization 7.3 Observer design 7.4 Applications 7.5 Examples
Chapter 8. Optimal Control
8.1 Performance criteria 8.2 Linear quadratic regulator 8.3 Riccati equations 8.4 Applications 8.5 Examples
Chapter 9. Robust Control
9.1 Uncertainty models 9.2 Stability margins 9.3 H-infinity methods (overview) 9.4 Applications 9.5 Examples
Part IV. Nonlinear Systems
Chapter 10. Nonlinear Dynamics
10.1 Phase space analysis 10.2 Equilibria 10.3 Stability 10.4 Applications 10.5 Examples
Chapter 11. Lyapunov Methods
11.1 Lyapunov functions 11.2 Invariance principles 11.3 Applications 11.4 Examples 11.5 Connections
Chapter 12. Nonlinear Control
12.1 Feedback linearization 12.2 Sliding mode control 12.3 Adaptive control 12.4 Applications 12.5 Examples
Part V. Discrete and Hybrid Systems
Chapter 13. Discrete-Time Systems
13.1 Difference equations 13.2 Stability 13.3 Z-transform methods 13.4 Applications 13.5 Examples
Chapter 14. Hybrid Systems
14.1 Continuous-discrete interaction 14.2 Switching systems 14.3 Applications 14.4 Examples 14.5 Connections
Chapter 15. Digital Control
15.1 Sampling 15.2 Quantization 15.3 Implementation issues 15.4 Applications 15.5 Examples
Part VI. Estimation and Filtering
Chapter 16. State Estimation
16.1 Observers 16.2 Kalman filter 16.3 Extended Kalman filter 16.4 Applications 16.5 Examples
Chapter 17. Stochastic Control
17.1 Random disturbances 17.2 Stochastic models 17.3 Control strategies 17.4 Applications 17.5 Examples
Chapter 18. System Identification
18.1 Model estimation 18.2 Parameter fitting 18.3 Validation 18.4 Applications 18.5 Examples
Part VII. Applications
Chapter 19. Engineering Systems
19.1 Mechanical systems 19.2 Electrical systems 19.3 Aerospace control 19.4 Applications 19.5 Examples
Chapter 20. Robotics
20.1 Motion control 20.2 Path planning 20.3 Feedback systems 20.4 Applications 20.5 Examples
Chapter 21. Networks and Large Systems
21.1 Distributed control 21.2 Network dynamics 21.3 Multi-agent systems 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Nonlinear control theory 22.2 Data-driven control 22.3 Learning-based control 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Robustness limits 23.2 Nonlinear stabilization 23.3 High-dimensional systems 23.4 Computational challenges 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of control theory 24.2 Key contributors 24.3 Evolution of systems theory 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Stability criteria summary B. Control design formulas C. Proof techniques checklist D. Algorithm templates E. Cross-reference to other MSC branches