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Dynamic Systems and Control

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Dynamic Systems and Control

The text addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.

Industrial and Systems EngineeringEngineering
Author
Mohammed Dahleh, Munther A. Dahleh, and George Verghese
Publisher
Massachusetts Institute of Technology
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Read online Download PDF (open licence)
Contents· 130 sections
  1. 01: Linear Algebra Review
  2. 1.01: Introduction
  3. 1.02: Vector Spaces
  4. 1.03: The Projection Theorem
  5. 1.04: Matrices
  6. 1.05: Linear Systems of Equations
  7. 1.06: Exercises
  8. 02: Least Squares Estimation
  9. 2.01: Introduction to Least Squares Estimation
  10. 2.02: Computing the Estimate
  11. 2.03: Preliminary- The Gram Product
  12. 2.04: The Least Squares Estimation Problem
  13. 2.05: The Projection Theorem and the Least Squares Estimate
  14. 2.06: Recursive Least Squares (optional)
  15. 2.07: Exercises
  16. 03: Least squares solution of y A x
  17. 3.01: Introduction
  18. 3.02: Constructing all Solutions
  19. 3.03: Least Squares Solution
  20. 3.04: Exercises
  21. 04: Matrix Norms and Singular Value Decomposition
  22. 4.01: Introduction
  23. 4.02: Matrix Norms
  24. 4.03: Singular Value Decomposition
  25. 4.04: Relationship to Matrix Norms
  26. 4.05: Exercises
  27. 05: Matrix Perturbations
  28. 5.01: Additive Perturbation
  29. 5.02: Multiplicative Perturbation
  30. 5.03: Perturabtions Measured in the Frobenius Norm
  31. 5.04: Total Least Squares
  32. 5.05: Conditioning of Matrix Inversion
  33. 5.06: Exercises
  34. 06: Dynamic Models
  35. 6.01: Introduction- Signals Systems and Models
  36. 6.02: System Representations
  37. 6.03: Exercises
  38. 07: State-Space Models
  39. 7.01: Introduction
  40. 7.02: General Description
  41. 7.03: Linearization
  42. 7.04: Exercises
  43. 08: Simulation and Realization
  44. 8.01: Introduction
  45. 8.02: Realization from I O Representations
  46. 8.03: Realization from an LTI Differential Difference equation
  47. 8.04: Exercises
  48. 09: New Page
  49. 10: Discrete-Time Linear State-Space Models
  50. 10.01: Time-Varying Linear Models
  51. 10.02: Linear Time-Invariant Models
  52. 10.03: Exercises
  53. 11: Continuous-time linear state-space models
  54. 11.01: The Time Varying Case
  55. 11.02: The LTI Case
  56. 11.03: Exercises
  57. 12: Modal decomposition of state-space models
  58. 12.01: The Transfer Function Matrix
  59. 12.02: Similarity Transformations
  60. 12.03: Solution in Modal Coordinates
  61. 12.04: Exercises
  62. 13: Internal (Lyapunov) Stability
  63. 13.01: Notions of Stability
  64. 13.02: Stability of Linear Systems
  65. 13.03: Lyapunov's Direct Method
  66. 13.04: Exercises
  67. 14: Internal stability for LTI systems
  68. 14.01: Quadratic Lyapunov Functions for LTI Systems
  69. 14.02: Lypanunov's Indirect Method- Analyzing the Linearization
  70. 14.03: Exercises
  71. 15: External input-output stability
  72. 15.01: Signal Measures
  73. 15.02: Input- Output Stability
  74. 15.03: Exercises
  75. 16: New Page
  76. 17: Interconnected systems and feedback- well-posedness stability and performance
  77. 17.01: System Interconnections
  78. 17.02: Well Posedness
  79. 17.03: External Stability
  80. 17.04: A More General Description
  81. 17.05: Obtaining Stability and Performance- A Preview
  82. 17.06: Exercises
  83. 18: Performance of feedback systems
  84. 18.01: SISO Loop Shaping
  85. 18.02: MIMO Loop Shaping
  86. 18.03: Algebraic Constraints
  87. 18.04: Analytic Constraints- The Waterbed Effect
  88. 18.05: Exercises
  89. 19: Robust stability in SISO systems
  90. 19.01: Additive Representation of Uncertainity
  91. 19.02: Multiplicative Representation of Uncertainty
  92. 19.03: The Nyquist Criterion
  93. 19.04: Robust Stability
  94. 19.05: Exercises
  95. 20: Stability Robustness
  96. 20.01: Introduction
  97. 20.02: Additive Representation of Uncertainty
  98. 20.03: Multiplicative Representation of Uncertainty
  99. 20.04: More General Representation of Uncertainty
  100. 20.05: A Linear Fractional Description
  101. 20.06: The Small-Gain Theorem
  102. 20.07: Stability Robustness Analysis
  103. 20.08: Appendix
  104. 20.09: Exercises
  105. 21: Robust performance and introduction to the structured singular value function
  106. 21.01: Introduction
  107. 21.02: Robust Disturbance Rejection
  108. 21.03: The Structured Singular Value
  109. 21.04: Properties of the Structured Singular Value
  110. 21.05: Computation of mu
  111. 21.06: Robust Disturbance Rejection (SISO)
  112. 21.07: Rank-One mu
  113. 21.08: Exercises
  114. 22: Reachability of DT LTI systems
  115. 22.01: Introduction
  116. 22.02: The Reachability Problem
  117. 22.03: Modal Aspects
  118. 22.04: Exercises
  119. 23: New Page
  120. 24: Observability
  121. 24.01: 24.1 Introduction
  122. 24.02: Observability
  123. 24.03: Discrete-Time Analysis
  124. 24.04: Continuous Time Analysis
  125. 25: Minimal state-space realization
  126. 26: Balanced Realization
  127. 27: Poles and zeros of MIMO systems
  128. 28: Stabilization- state feedback
  129. 29: Observers model-based controllers
  130. 30: Minimality and stability of interconnected systems