The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We
will learn from convex sets, convex functions and then proceed to definition of LMIs in control theory. Thereafter, we present
the system analysis (focusing on stability) and design (focusing on stabilization and robustness) with LMIs. Numerical simulations
are also described and practiced in MATLAB and Simulink.

- Can understand convex sets, convex functions and basic idea of convex programming
- Can understand the definition and properties of LMIs, together with basic simulation for solving LMIs
- Can understand the idea and procedure of using LMIs in analysis and design of modern control systems

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1． | Course guidance, history of LMIs in modern control theory | Comparison between classic and modern control | 190minutes |

2． | State space representation (SSR) of modern control systems, Solutions of SSR | Review of differential equations, Laplace transform | 190minutes |

3． | Stability and and robust stability of control systems | Review eigenvalues of matrices and system response (trajectory); Review norm of vectors and matrices | 190minutes |

4． | Convex sets, convex functions, convex programming; Review and Report 1 (system modeling, solution and stability) | Review Week 1-3, convex sets and convex function in calculus | 190minutes |

5． | Definition and properties of LMIs, Stability analysis with LMIs | Review positive (negative) definite properties of symmetric matrices; Review stability concept and system behavior | 190minutes |

6． | Robust stability analysis with LMIs; LMI based stabilization via state feedback | Review the basic idea of state feedback in control systems | 190minutes |

7． | LMI based robust stabilization via state feedback (polytopic uncertainties) ; Review and Report 2 | Try to understand system uncertainty and how to evaluate uncertainty; Review of the whole course | 190minutes |

8． | None | None | 0minutes |

9． | None | None | 0minutes |

10． | None | None | 0minutes |

11． | None | None | 0minutes |

12． | None | None | 0minutes |

13． | None | None | 0minutes |

14． | None | None | 0minutes |

Total. | - | - | 1330minutes |

Report 1 | Report 2 | Total. | |
---|---|---|---|

1. | 40% | 40% | |

2. | 30% | 30% | |

3. | 30% | 30% | |

Total. | 40% | 60% | - |

Report 1: 40%

Report 2: 60%

-------------------

PASS when reaching 60% of the whole evaluation, or in other words, understanding how to use and solve LMIs in stability analysis and stabilization with state feedback.

Report 2: 60%

-------------------

PASS when reaching 60% of the whole evaluation, or in other words, understanding how to use and solve LMIs in stability analysis and stabilization with state feedback.

No text books; Will deliver handouts and suggest several reference books

【1】岩崎徹也：ＬＭＩと制御，昭晃堂，1997 (ISBN 4785690534)

【2】Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004

(http://www.stanford.edu/~boyd/cvxbook/) (ISBN 978-0-521-83378-3)

【3】Boyd, El Ghaoui, Feron, Balakrishnan: Linear Matrix Inequalities in System and Control Theory, SIAM, 1994 (http://www.stanford.edu/~boyd/lmibook/lmibook.pdf)

(ISBN 0-89871-334-X)

【4】川田昌克：MATLAB/Simulinkによる現代制御入門，森北出版，2011 (ISBN 9784627920415)

【1】岩崎徹也：ＬＭＩと制御，昭晃堂，1997 (ISBN 4785690534)

【2】Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004

(http://www.stanford.edu/~boyd/cvxbook/) (ISBN 978-0-521-83378-3)

【3】Boyd, El Ghaoui, Feron, Balakrishnan: Linear Matrix Inequalities in System and Control Theory, SIAM, 1994 (http://www.stanford.edu/~boyd/lmibook/lmibook.pdf)

(ISBN 0-89871-334-X)

【4】川田昌克：MATLAB/Simulinkによる現代制御入門，森北出版，2011 (ISBN 9784627920415)

- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic self-management skills
- Course that cultivates a basic problem-solving skills

Work experience | Work experience and relevance to the course content if applicable |
---|---|

N/A | N/A |

Last modified : Tue Mar 23 04:07:54 JST 2021