¡®Robust control ¡¯ introduces the basic components and methods of robust control to the graduate students; the main content includes: systems¡¯ performance index, stability of feedback systems, robust analysis and control of the uncertainty systems, linear fraction transformation(LFT), structure singular value(SSV), Riccati equation theory, the controller design of the optimization of input/output norm index etc. The course needs the basic knowledge of modern control theory and linear algebra. The goal is mastering the basic methods in the robust control, designing the controller and reading the frontier papers readily.
Chapter 1 Introduction
Introduce the object, problems, methods and the basic structure in the robust control.
Chapter 2 H2 and H¡Þ space
2.1 Inner product space and Hilbert space
2.2 H2 and H¡Þ space
2.3 Calculation of the norm of L2 and H2
2.4 Calculation of the norm of L¡Þ and H¡Þ
Chapter 3 Internal stability
3.1 Feedback structure
3.2 Well-posedness of feedback loop
3.3 Internal stability
3.4 Coprime factorizaiton over RH¡Þ
Chapter 4 Performance specifications and limitations
4.1 Feedback properties
4.2 Weighted H2 and H¡Þ performance
4.3 Selction of weighted functions
4.4 Bode gain and phrase relation
4.5 Bode¡¯s sensitivity integral
4.6 Analyticity constraints
Chapter 5 Balanced model reduction
5.1 Lypunov equations
5.2 Balanced realization
5.3 Model reduction based on balanced truncation
5.4 Frequency-weighted balanced model reduction
Chapter 6 Controller parameterizaiton
6.1 Existence of stabilizing controllers
6.2 Youla parameterizaiton of controllers
Chapter 7 Algebraic Raccati equations
7.1 Stabilizing solution of the Raccati operator
7.2 Bounded real lemma
Chapter 8 H2 optima control
8.1 Introduction to regular problems
8.2 Standard LQR problem
8.3 Extended LQR problem
8.4 Guaranteed stability margins of LQR
8.5 Standard H2 problem
8.6 State feedback H2 synthesis of LMI
Chapter 9 H¡Þ synthesis
9.1 Two insignificant inequalities and KYP lemma
9.2 H¡Þ synthesis
9.3 Designation of controller
Chapter 10 Systems with uncertainties
10.1 Uncertainty
10.2 Small gain theory
10.3 Uncertainty model and robust stability
10.4 Arbitrary block stuctured uncertainty, S-process of L2
10.5 Structured singular value
10.6 Time invariant uncertainties