A A 598
Introduction of special topics in the field of aeronautics and astronautics. Topics introduced by regular and guest speakers and includes a variety of information that is of current interest in aeronautics and astronautics. Offered: AWSp.
(1) System Models: Linearity, Linearization, Finite Dimensionality, Time-Varying vs. Time-Invariant Linear Systems, Interconnection of Linear Systems
(2) State-Space and Input-Output Descriptions: State-Space Model, Frequency-Domain Model: Transfer Function, Frequency Responses.
(3) Responses of Continuous- and Discrete-Time Systems: State Transition Matrix, Exponential Matrix, Time Convolution Integral, Natural and Forced Responses.
(4) Stability of Linear Systems: Eigenvalues and Generalized Eigenvectors, Nyquist Stability, Lyapunov Stability.
(5) Multivariable System Properties: System Norms, Singular Value Analysis, System Zeros, System Controllability, System Observability, System Invertibility.
(6) Realization Theory
Student learning goals
Know how to represent a linear system in both time and frequency domains.
Know how to analyze responses of a linear system to initial conditions and arbitrary external inputs.
Know how to determine whether a linear system is stable using eigenvalues, Lyapunov stability criterion and Nyquist stability criterion.
Determine whether a linear system is controllable, identify all the controllable and uncontrollable modes of the system, transform the linear system model into controllable canonical form.
Determine whether a linear system is observable, identify all the observable and unobservable modes of the system, transform the linear system model into observable canonical form.
Know to realize a state-space model from a transfer function description.
General method of instruction
Lectures, Homeworks, Exams.
Review the subjects of ordinary differential equations, linear algebra (matrix theory), Laplace, Fourier and z-transforms, classical control theory.
Class assignments and grading
Homework assignments are designed to illustrate concepts covered in the class lectures through applications to mathematical and engineering problems. Matlab and other computational softwares will be introduced to solve complex mathematical problems and analyze high-order linear dynamical systems.
Class grade will be based on (1) Homework: 30% (2) Midterm: 30% (3) Final: 30% (4) Others: 10% (e.g., project, extra effort, interaction in class, etc,...)