ECE 515: Lecture Schedule

The schedule will be updated and revised as the course progresses. Required readings from the course notes will be indicated on the left.

System modeling and analysis

Tue Aug 22
Ch. 1
Introduction and administrivia
State-space models
Linearization about an equilibrium point
Linearization about a trajectory
Thu Aug 24
Ch. 1
Input-output description of SISO LTI systems using transfer functions
State-space realization
Controllable, observable, modal canonical forms
Tue Aug 29
Ch. 2
Fields and vector spaces
Linear independence, bases, dimension
Change of basis
Linear operators and matrices
Thu Aug 31
Ch. 2
Linear operators: nullspace and range
Eigenvalues and eigenvectors
Diagonalization and Jordan canonical form
Tue Sep 5
Ch. 3
Solving state-space equations
State transition matrix
Matrix exponential
The Cayley-Hamilton theorem
Thu Sep 7
Ch. 3
Solving state-space equations: time-varying systems
The fundamental matrix and the state transition matrix
Peano-Baker series

System structural properties

Tue Sep 12
Ch. 4
Motivating example: external vs. internal stability, pole-zero cancellation
Stability in the sense of Lyapunov
Asymptotic and global asymptotic stability
Stability criteria for LTI systems
Lyapunov's direct method
LaSalle's invariance theorem
Thu Sep 14
Ch. 4
Stability (cont.)
Stability of linear time-invariant systems
Lyapunov equation
Nonlinear systems and linearization
Hartman-Grobman theorem (the easy part)
Input-output stability
Tue Sep 19
Ch. 5
Motivation and definition
The general LTV case: the controllability Gramian
Thu Sep 21
Ch. 5
Controllability (cont.)
Controllability of linear time-invariant systems
Controllability matrix, rank criterion
Tue Sep 26
Thu Sep 28
No class: Allerton conference

Tue Oct 3
Ch. 5, 6
Controllability (cont.) and intro to observability
Other tests for controllability
Modal form, the Hautus-Rosenbrock criterion
Observability: motivation and definition
The observability matrix
The general LTV case: the observability Gramian
Thu Oct 5
Ch. 6
Observability (cont.)
Duality between controllability and observability
Kalman canonical forms
Realization of transfer functions
Minimal (controllable and observable) realization


Tue Oct 10
Ch. 7
Pole placement
Kalman's canonical forms revisited
Stabilizability and closed-loop pole placement
Detectability and observer pole placement
Duality between controllability/observability and between stabilizability/detectability
Thu Oct 12
No class
Tue Oct 17
Ch. 7
Pole placement (cont.)
Dynamic output feedback
The separation principle
Reduced-order (Luenberger) observers
Thu Oct 19

System invariants
Similarity and feedback equivalence
Canonical forms revisited
Controllability indices
Tue Oct 24
Ch. 8
Tracking and disturbance rejection
Internal model principle
Conditions in terms of controllability
Transfer function approach: Sylvester systems
Tue Oct 26
Ch. 9
Internal model principle revisited
IMP for linear time-invariant systems (see Section 1 of E.D. Sontag, "Adaptation and regulation with signal detection implies internal model")
Control goals: stability, regulation/tracking, transient response shaping, robustness
Sensitivity to plant model misspecification and disturbances
Fundamental limitations: Bode's sensitivity integral
Tue Oct 30
In-class review and Q&A
Thu Nov 1

No class: Take-home midterm!

Optimal Control

Tue Nov 7
Ch. 10
Dynamic progamming
Formulation of the finite-horizon optimal control problem
Bellman's dynamic programming principle
The Hamilton-Jacobi-Bellman equation
The Linear Quadratic Regulator (LQR) problem: formulation and derivation of optimal control using completion of squares