Linear Systems and Optimization |
Introduction to Linear Dynamical Systems
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.
Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.
Prerequisites: Exposure to linear algebra and matrices (as in Math. 103). You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.
Stephen P. Boyd is the Samsung Professor of Engineering, and Professor of Electrical Engineering in the Information Systems Laboratory at Stanford University. His current research focus is on convex optimization applications in control, signal processing, and circuit design.
Professor Boyd received an AB degree in Mathematics, summa cum laude, from Harvard University in 1980, and a PhD in EECS from U. C. Berkeley in 1985. In 1985 he joined the faculty of Stanford’s Electrical Engineering Department. He has held visiting Professor positions at Katholieke University (Leuven), McGill University (Montreal), Ecole Polytechnique Federale (Lausanne), Qinghua University (Beijing), Universite Paul Sabatier (Toulouse), Royal Institute of Technology (Stockholm), Kyoto University, and Harbin Institute of Technology. He holds an honorary doctorate from Royal Institute of Technology (KTH), Stockholm.
Professor Boyd is the author of many research articles and three books: Linear Controller Design: Limits of Performance (with Craig Barratt, 1991), Linear Matrix Inequalities in System and Control Theory (with L. El Ghaoui, E. Feron, and V. Balakrishnan, 1994), and Convex Optimization (with Lieven Vandenberghe, 2004).
Professor Boyd has received many awards and honors for his research in control systems engineering and optimization, including an ONR Young Investigator Award, a Presidential Young Investigator Award, and an IBM faculty development award. In 1992 he received the AACC Donald P. Eckman Award, which is given annually for the greatest contribution to the field of control engineering by someone under the age of 35. In 1993 he was elected Distinguished Lecturer of the IEEE Control Systems Society, and in 1999, he was elected Fellow of the IEEE, with citation: “For contributions to the design and analysis of control systems using convex optimization based CAD tools.” He has been invited to deliver more than 30 plenary and keynote lectures at major conferences in both control and optimization.
In addition to teaching large graduate courses on Linear Dynamical Systems, Nonlinear Feedback Systems, and Convex Optimization, Professor Boyd has regularly taught introductory undergraduate Electrical Engineering courses on Circuits, Signals and Systems, Digital Signal Processing, and Automatic Control. In 1994 he received the Perrin Award for Outstanding Undergraduate Teaching in the School of Engineering, and in 1991, an ASSU Graduate Teaching Award. In 2003, he received the AACC Ragazzini Education award, for contributions to control education, with citation: “For excellence in classroom teaching, textbook and monograph preparation, and undergraduate and graduate mentoring of students in the area of systems, control, and optimization.”
Complete Course Material Downloads:Course Handouts: The ZIP file below contains all of the course handouts for this course. If you do not need the complete course, individual documents can be downloaded from the course content pages.
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