ECE 501: Lecture Notes - Fall 2002

• Lecture Note #1, Superposition principle, state-space representation (Monday, August 26, 2002)
• Lecture Note #2, Transfer function -> state-space description, strictly proper systems, proper systems, non-proper systems, similarity transformations, state-space description -> transfer function, controller-canonical form (Wednesday, August 28, 2002)
• Lecture Note #3, Input decoupling of uncontrollable modes, output decoupling of unobservable modes (Wednesday, September 4, 2002)
• Lecture Note #4, Kalman decomposition, duality principle observer-canonical form (Wednesday, September 9, 2002)
• Lecture Note #5, Solution in the time domain, convolution integral, matrix exponential, Markov parameters (Wednesday, September 11, 2002)
• Lecture Note #6, Controllability, observability, the Nordsieck vector, controllability canonical form, observability canonical form (Wednesday, September 16, 2002)
• Lecture Note #7, Toeplitz and Hankel matrices, eigenvalues and eigenvectors (Wednesday, September 18, 2002)
• Lecture Note #8, Jordan canonical form, single eigenvalues, multiple eigenvalues with multiple eigenvectors (Monday, September 23, 2002)
• Lecture Note #9, Jordan canonical form, multiple eigenvalues with single eigenvectors, generalized eigenvectors, images and nullspaces (Wednesday, September 25, 2002)
• Lecture Note #10, QR-decomposition, transcendental functions, Cayley-Hamilton theorem (Wednesday, October 2, 2002)
• Lecture Note #11, Hermitian forms and matrices, singular value decomposition, vector and matrix norms, inner and outer vector products (Monday, October 7, 2002)
• Lecture Note #12, State and output feedback designs, pole placement, n^th-order Luenberger observer (Wednesday, October 9, 2002)
• Lecture Note #13, Selection of pole locations, balancing of controller and observer gains, functional observer (Monday, October 14, 2002)
• Lecture Note #14, Optimal control, variational principle, Euler equation, lagrange equation, transversality condition, Hamiltonian, maximum principle of Pontryagin (Wednesday, October 16, 2002)
• Lecture Note #15, Linear state feedback by optimal control, matrix-Riccati equation, Hamiltonian matrix, output weighting, exponential stability, observer design using optimal control, balancing controller and observer gains (Wednesday, October 23, 2002)
• Lecture Note #16, Steady-state accuracy, augmented state feedback, disturbance suppression, Kalman-Bucy filter (Monday, October 28, 2002)
• Lecture Note #17, MIMO systems, transformation into frequency domain, pole-zero cancellations vs. controllability and observability, polynomial degree vs. system order, Gilbert diagonal realization, Jordan-canonical form (Wednesday, October 30, 2002)
• Lecture Note #18, Controller- and observer-canonical realizations of MIMO systems, transformation into controller- and observer-canonical forms, input decoupling of uncontrollable modes, output-decoupling of unobservable modes, decoupling of insignificant inputs and outputs (Monday, November 4, 2002)
• Lecture Note #19, Controller design for MIMO systems by pole placement, observer design for MIMO systems using full-order and minimal-order Luenberger observers (Wednesday, November 6, 2002)
• Lecture Note #20, Polynomial matrix representation, elementary operations, unimodular operations, LU-decomposition, equivalence transformations (Monday, November 18, 2002)
• Lecture Note #21, Smith decomposition, Smith-McMillan form, dividers of polynomial matrices, transfer and equivalence relations (Wednesday, November 20, 2002)
• Lecture Note #22, Controllability and observability of polynomial matrix representations, poles and zeros, structure theorem, controller-canonical realization, observer-canonical realization (Monday, November 25, 2002)
• Lecture Note #23, State-space realization of a polynomial matrix representation, controller-canonical and observer-canonical polynomial matrix realizations of a transfer function matrix (Wednesday, November 27, 2002)
• Lecture Note #24, Compensator design in the frequency domain (Monday, December 9, 2002)
• Lecture Note #25, General compensations techniques, division algorithm for polynomial matrices, general decoupling and model reduction (Wednesday, December 11, 2002)