Electrical, Computer, and Systems Engineering Department

ECSE 6460 Multivariable Control, FALL 2004

Lecture Slides

8/30/04:           Lecture 01: Introduction   inverted pendulum video (from IROS 02)

9/2/04:             Lecture 02: Linear algebra  inclass  hw#1 related

9/9/04:             Lecture 03: Description of linear time invariant systems

9/13/04:           Lecture 04: Controllability, observability, observer based control design   inclass

Randy Beard, “Linear Operator Equations with Applications in Control and Signal Processing IEEE Control Systems Magazine, April, 2002,  pages 69-79.  (on orthogonal decomposition and application to least square problems in systems and control).

9/16/04:           We are running behind, so we’ll cover the lecture #4 materials today.  inclass

9/20/04:           Lecture 06: poles, zeros, and matrix fractional description (MFD)  inclass 

Copy of part of Ch. 2 of Maciejowski (on Smith-McMillan form)

9/23/04:           We are covering lecture #6 materials today.  inlcass

9/27/04:           Lecture 08: realization  inlcass

Lyapack link: http://www.tu-chemnitz.de/sfb393/lyapack/  (approximate balanced realization and truncation toolbox)

9/30/04:           Class cancelled (HW#3 due on 10/4).

10/4/04:           Lecture 09: identification, model reduction   inlcass

T. McKelvey, H. Akcay, L. Ljung, “Subspace-based Multivariable Systems Identification from Frequency Response Data,” IEEE Transaction on Automatic Control, 41(7), July, 1996, pp.960-979.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

A.C. Antoulas, “Approximation of linear dynamical systems,” Encyclopedia of Electrical and Electronics Engineering, ed. J.G. Webster, John Wiley and Sons, 1999, pp.403-422.the

10/7/04:           Lecture 10: signals and systems inclass

10/12/04:         Continued with Lecture 10 inclass

10/14/04:         Lecture 12: more on model reduction, stability of interconnected systems, multivariable Nyquist criterion  inclass

                        Stochastic balanced realization:

                        M. Green, “A Relative Error Bound for Balanced Stochastic Truncation,” IEEE Trans. on Automatic Control, 33(10), October 1988, pp.961-965.

                        U.B. Desai and D. Pal, “A Transformation Approach to Stochastic Model Reduction,” IEEE Trans. on Automatic Control, 29(12), December 1984, pp.1097-1100.

10/18/04:         Lecture 13: Examples of using multivariable Nyquist criterion, robust stability criteria, structured singular values  inclass

10/21/04:         Continued with Lecture 13  inclass

10/25/04:         Lecture 15: Parameterization of all stabilizing controllers  inclass

10/28/04:         Continued with Lecture 15  inclass

11/1/04:           Lecture 17: Loop shaping, Bode integral formula

11/4/04:           Lecture 18: H2 optimization (full state feedback case)  inclass

11/8/04:           Lecture 19: Algebraic Riccati Equation  inclass

                        Positive realness condition:

                        J.T. Wen, “Time domain and frequency domain conditions for strict positive realness,” IEEE Trans. on Automatic Control, 33(10), Oct, 1988, pp.988-992.

11/11/04:         Lecture 20: H2 optimization, general output feedback case inclass

11/15/04:         Lecture 21: Robustness of H2 optimal controller (guarantee gain/phase margins for full state feedback case, loop transfer recovery for output feedback case) inclass

11/18/04:         class cancelled (please hand in homework the following Monday, 11/22)

11/22/04:         Lecture 22: H optimization, full state feedback case inclass

11/29/04:         Lecture 23: H optimization, general output feedback case  inclass

12/2/04:           Lecture 24: Robust performance, µ synthesis  inclass

12/6/04:           Lecture 25: Gap metric  inclass

12/9/04:           Lecture 26: Recap

 Other Useful Materials

Feedback Control Theory by Doyle, Francis, Tannenbaum (Originally published by Macmillan in 1990 but is now out of print.  The authors have generously put the pdf file on-line)


Mailing Address:

John T. Wen
Office: CII 8213
Voice: (518)-276-8744
Fax: (518)-276-4897
Email: wen@cat.rpi.edu