Lecture Notes on Linear System Theory
(University of Arizona)
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Lecture Note #1, Superposition principle, state-space
representation (Monday, August 26, 2002)
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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)
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Lecture Note #3, Input decoupling of uncontrollable modes,
output decoupling of unobservable modes
(Wednesday, September 4, 2002)
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Lecture Note #4, Kalman decomposition, duality principle
observer-canonical form
(Wednesday, September 9, 2002)
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Lecture Note #5, Solution in the time domain, convolution
integral, matrix exponential, Markov parameters
(Wednesday, September 11, 2002)
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Lecture Note #6, Controllability, observability,
the Nordsieck vector, controllability canonical form,
observability canonical form
(Wednesday, September 16, 2002)
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Lecture Note #7, Toeplitz and Hankel matrices,
eigenvalues and eigenvectors
(Wednesday, September 18, 2002)
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Lecture Note #8, Jordan canonical form, single
eigenvalues, multiple eigenvalues with multiple eigenvectors
(Monday, September 23, 2002)
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Lecture Note #9, Jordan canonical form, multiple
eigenvalues with single eigenvectors, generalized eigenvectors,
images and nullspaces
(Wednesday, September 25, 2002)
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Lecture Note #10, QR-decomposition, transcendental functions,
Cayley-Hamilton theorem
(Wednesday, October 2, 2002)
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Lecture Note #11, Hermitian forms and matrices, singular
value decomposition, vector and matrix norms, inner and
outer vector products
(Monday, October 7, 2002)
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Lecture Note #12, State and output feedback designs,
pole placement, nth-order Luenberger observer
(Wednesday, October 9, 2002)
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Lecture Note #13, Selection of pole locations, balancing
of controller and observer gains, functional observer
(Monday, October 14, 2002)
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Lecture Note #14, Optimal control, variational principle,
Euler equation, lagrange equation, transversality condition,
Hamiltonian, maximum principle of Pontryagin
(Wednesday, October 16, 2002)
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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)
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Lecture Note #16, Steady-state accuracy, augmented state
feedback, disturbance suppression, Kalman-Bucy filter
(Monday, October 28, 2002)
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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)
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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)
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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)
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Lecture Note #20, Polynomial matrix representation,
elementary operations, unimodular operations,
LU-decomposition, equivalence transformations
(Monday, November 18, 2002)
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Lecture Note #21, Smith decomposition, Smith-McMillan
form, dividers of polynomial matrices, transfer and
equivalence relations
(Wednesday, November 20, 2002)
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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)
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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)
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Lecture Note #24, Compensator design in the frequency
domain
(Monday, December 9, 2002)
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Lecture Note #25, General compensations techniques,
division algorithm for polynomial matrices, general
decoupling and model reduction
(Wednesday, December 11, 2002)
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Last modified: June 24, 2005 -- © François Cellier