课程名称 (Course Name) ： Linear System

课程代码 (Course Code）： X032504

学分/学时 (Credits/Credit Hours)： 3

开课时间 (Course Term )：  Fall

开课学院（School Providing the Course）:  JI

任课教师（Teacher）:  Zhang Jun

课程讨论时数（Course Discussion Hours）:  

课程实验数（Lab Hours）:   

课程内容简介(Course Introduction):

Through the study of this course, the students are required to:

1.Master the fundamental knowledge and the analytic methods of linear system theory, be able to describe the system by state space representation and establish the state space representation according to the differential equation of the system.

2.Master the methods to obtain the characteristic roots of the system, the solution to the inhomogeneous equation in linear time-invariant and linear time-variant system, and two methods to solve the state equation in the discrete time system.

3.Master the definition of controllability and observability and its respective criteria.

4. Master the methods to analyze the stability of a system by Lyapunov first method and Lyapunov second method.

5. Master the basic design methods of state feedback and state observer.

6. Master the fundamentals of the frequency domain theory.

7. Have a general understanding of the new development in the linear system theory.

Homepage: www.umji.sjtu.edu.cn

1 Tel: 86-21-34206190

Fax: 86-21-34206525

教学大纲(Course Teaching Outline):

Review of Basic Algebra: Rings, fields, vector spaces, matrices, basis, dimensions of vector spaces, properties of linear maps, norms, induced norms.

Differential Equation: Linear, finite dimensional, and time varying system, state transition matrix, properties of the state transition matrix; the adjoint equation and the variational equation, linear time invariant case.

Matrices and their eigenspaces: Left and right eigenvectors, eigenvalues, invariant subspaces, direct sum of subspaces, minimal polynomials, generalized eigenvectors and the Jordan decomposition theorem, functions of a matrix and the spectral mapping theorem

Numerical Considerations: Hermitian matrices, adjoints, singular value decomposition, condition number of a matrix

Controllability and Observability: Characterization, effects of feedback, output injection,

coduality, minimality and the Kalman decomposition, realization, Hankel and Toeplitz matrices,

stabilizability, detectability, interval and I/O stability

State Feedback and State Estimation: Eigenvalue assignment by state feedback, full order and reduced order observers, separation principle for output based pole placement

Linear Quadratic Optimal Control: Least squares control and estimation, Riccati equations and properties of the Linear Quadratic Regulator

Stability: BIBO stability, state space stability, Lyapunov condition

课程进度计划(Course Schedule):

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课程考核要求(Course Assessment Requirements)：

Your work in this course includes: attending lecture, reading assigned material, completing homework assignments and two exams. Final grades will be based on the total points earned on the homework and exams. The weight assigned to each category is as follows:

Homework: 30 %

Midterm: 30 %

Final: 35 %

Participancy: 5%

Those students who miss 1/3 of the lectures will be failed automatically.

参考文献(Course References)：

Systems:

• Frank M. Callier and Charles A. Desoer, Linear Systems, Springer-Verlag, 1991.

• Jo˜ao P. Hespanha, Linear Systems Theory, Princeton University Press, 2009.

• Chi-Tsong Chen, Linear Systems Theory and Design, Oxford University Press, 1998.

• Thomas Kailath, Linear Systems Theory, Prentice-Hall, 1980.

Algebra:

• Gilbert Strang, Linear Algebra and its Applications, 4th edition, Brooks Cole, 2005.

• David C. Lay, Linear Algebra and its Applications, 4th edition, Pearson, 2011.

Analysis:

• Halsey Royden, Real Analysis, 3rd edition, Pearson, 1988.

预修课程（Prerequisite Course）