A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models.
The book supports that in H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some non-regular cases.
This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory.
1. 1: Introduction - p. iv 2. 2: Mathematical preliminaries - p. 10 3. 3: Generalized inverse of matrix and solution of linear system equation - p. 37 4. 4: Polynomial fraction description - p. 50 5. Abstract - p. 50 6. 4.1 Introduction - p. 50 7. 4.2 Right polynomial fractions - p. 52 8. 4.3 Left polynomial fraction - p. 58 9. 4.4 Column and row degrees - p. 62 10. 4.5 Minimal realization - p. 66 11. 4.6 Poles and zeros - p. 71 12. 4.7 State feedback - p. 75 13. 5: Stability - p. 76 14. 6: Fundamental approaches to control system analysis - p. 103 15. 7: Determination of finite and infinite frequency structure of a rational matrix - p. 118 16. Abstract - p. 118 17. 7.1 Introduction - p. 118 18. 7.2 The Toeplitz rank information - p. 120 19. 7.3 To determine the Smith form of a polynomial matrix - p. 129 20. 7.4 To determine the Smith-McMillan form at infinity of a rational matrix - p. 130 21. 7.5 To determine the Smith-McMillan form of a rational matrix - p. 134 22. 7.6 Conclusions - p. 139 23. 8: The solution of a regular PMD and the set of impulsive free initial conditions - p. 140 24. Abstract - p. 140 25. 8.1 Introduction - p. 140 26. 8.2 Preliminary results - p. 143 27. 8.3 A solution for the LNHMDEs - p. 144 28. 8.4 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is of full row rank - p. 147 29. 8.5 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is not of full row rank - p. 151 30. 8.6 Illustrative example - p. 154 31. 8.7 Conclusions - p. 159 32. 9: A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs - p. 159 33. Abstract - p. 159 34. 9.1 Introduction - p. 159 35. 9.2 Infinite Jordan pairs - p. 162 36. 9.3 The solution of regular PMDs - p. 169 37. 9.4 Algorithm and examples - p. 175 38. 9.5 Conclusions - p. 188 39. 10: Frequency structures of generalized companion form and application to the solution of regular PMDs - p. 189 40. 11: A generalized chain-scattering representation and its algebraic system properties - p. 206 41. 12: Realization of behavior - p. 222 42. 13: Related extensions to system well-posedness and internal stability - p. 238 43. 14: Nonstandard H∞ control problem: A generalized chain-scattering representation approach - p. 256 44. 15: Internet congestion control: A linear multivariable control look - p. 271 45. Abstract - p. 271 46. 15.1 The basic model of Internet congestion control - p. 275 47. 15.2 Internet congestion control: A multivariable control look - p. 276 48. 15.3 Padé approximations to the system (15.7) and (15.8) - p. 277 49. 15.4 Analyses into system structure of congestion control of a simple network in frequency domain - p. 281 50. 15.5 Conclusions and further discussions - p. 290 51. 16: Conclusions and further research - p. 292 52. Bibliography - p. 298 53. Index - p. 307
A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models.
The book supports that in H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some non-regular cases.
This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory.
1. 1: Introduction - p. iv 2. 2: Mathematical preliminaries - p. 10 3. 3: Generalized inverse of matrix and solution of linear system equation - p. 37 4. 4: Polynomial fraction description - p. 50 5. Abstract - p. 50 6. 4.1 Introduction - p. 50 7. 4.2 Right polynomial fractions - p. 52 8. 4.3 Left polynomial fraction - p. 58 9. 4.4 Column and row degrees - p. 62 10. 4.5 Minimal realization - p. 66 11. 4.6 Poles and zeros - p. 71 12. 4.7 State feedback - p. 75 13. 5: Stability - p. 76 14. 6: Fundamental approaches to control system analysis - p. 103 15. 7: Determination of finite and infinite frequency structure of a rational matrix - p. 118 16. Abstract - p. 118 17. 7.1 Introduction - p. 118 18. 7.2 The Toeplitz rank information - p. 120 19. 7.3 To determine the Smith form of a polynomial matrix - p. 129 20. 7.4 To determine the Smith-McMillan form at infinity of a rational matrix - p. 130 21. 7.5 To determine the Smith-McMillan form of a rational matrix - p. 134 22. 7.6 Conclusions - p. 139 23. 8: The solution of a regular PMD and the set of impulsive free initial conditions - p. 140 24. Abstract - p. 140 25. 8.1 Introduction - p. 140 26. 8.2 Preliminary results - p. 143 27. 8.3 A solution for the LNHMDEs - p. 144 28. 8.4 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is of full row rank - p. 147 29. 8.5 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is not of full row rank - p. 151 30. 8.6 Illustrative example - p. 154 31. 8.7 Conclusions - p. 159 32. 9: A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs - p. 159 33. Abstract - p. 159 34. 9.1 Introduction - p. 159 35. 9.2 Infinite Jordan pairs - p. 162 36. 9.3 The solution of regular PMDs - p. 169 37. 9.4 Algorithm and examples - p. 175 38. 9.5 Conclusions - p. 188 39. 10: Frequency structures of generalized companion form and application to the solution of regular PMDs - p. 189 40. 11: A generalized chain-scattering representation and its algebraic system properties - p. 206 41. 12: Realization of behavior - p. 222 42. 13: Related extensions to system well-posedness and internal stability - p. 238 43. 14: Nonstandard H∞ control problem: A generalized chain-scattering representation approach - p. 256 44. 15: Internet congestion control: A linear multivariable control look - p. 271 45. Abstract - p. 271 46. 15.1 The basic model of Internet congestion control - p. 275 47. 15.2 Internet congestion control: A multivariable control look - p. 276 48. 15.3 Padé approximations to the system (15.7) and (15.8) - p. 277 49. 15.4 Analyses into system structure of congestion control of a simple network in frequency domain - p. 281 50. 15.5 Conclusions and further discussions - p. 290 51. 16: Conclusions and further research - p. 292 52. Bibliography - p. 298 53. Index - p. 307
