Course Contents During this course the following topics will be covered:
State-space representation of input-output system (both for continuous-time and discrete-time case).
Linearization of a system.
Solution of a linear system (both for continuous-time and discrete-time case).
Impulse response and step response of a linear system (both for continuous-time and discrete-time case).
Asymptotic stability, BIBO stability (both for continuous-time and discrete-time case).
Controllability and observability (both for continuous-time and discrete-time case).
Kalman decomposition.
State feedback (both for continuous-time and discrete-time case).
State reconstruction by observer (both for continuous-time and discrete-time case).
System description in frequency domain.
Composition of systems in frequency domain.
Realization of transfer function.
Study Goals After a successful completion of the course you will be able to
model an input-output system by a state space model (both for continuous-time and discrete-time case).
linearize a system around a given solution.
determine whether an equilibrium point of a linear system is asymptotically stable, weakly stable or unstable (both for
continuous-time and discrete-time case).
compute the solution of a linear time-invariant system (both for continuous-time and discrete-time case).
compute the impulse response and the step response of a linear time-invariant system (both for continuous-time and discrete-time
case).
determine whether or not a linear system is controllable (both for continuous-time and discrete-time case).
determine whether or not a linear system is observable (both for continuous-time and discrete-time case).
construct a Kalman decomposition of a linear system.
design a feedback control (if it exists) which makes an unstable system stable or one which reduces the effect of disturbing
signals (both for continuous-time and discrete-time case).
design an observer (if it exists) which produces an approximation of the state of the system such that the error converges to zero
(both for continuous-time and discrete-time case).
represent a linear system in the frequency domain.
construct various realizations of a given transfer function.
