Introduction to Discrete Linear Systems
Subject code: SIP 7013
Lecturer
Dr Sergey Simakov
Mode of delivery
On-line only.
Assumed knowledge
Linear algebra (matrices), a basic knowledge on differential equations
(linear systems) and complex analysis (Laplace transforms), probability
theory, MATLAB.
Aims/Learning Objectives
The course considers as two separate components the deterministic linear
systems and elements of linear stochastic modelling. Both components have
linkages with the linear control theory and signal processing techniques. The
students will become familiar with such fundamental concepts as the
reachability/controllability and observability of discrete- and continuous-time
linear systems in the time-invariant and general time-dependent cases. In the
second part of the course the students will be introduced to elements of
parametric modelling involving ARMA series and the use of the Yule-Walker
equations. Connection between the Autoregressive Modelling and linear
prediction (the Wiener filter) will be discussed in the examples.
The course exercises will give the students ample opportunity to review their
knowledge of linear systems and algebra, as well as to refine their MATLAB
skills and use them in the context of time-series modelling.
Content
Deterministic time-invariant linear systems:
discrete-time and continuous-time state vector equations
and state variable diagrams;
solution of state vector equations, matrix exponentials, state-transition
matrices; controllability and observability; solution by Z-transforms
and Laplace transforms, transfer functions; stability,asymptotic
stability, state feedback and pole placement.
Introduction to stochastic linear systems:
stochastic processes, ergodic series, autocorrelation function,
the ARMA model, special cases of the ARMA process,
Yule-Walker equations and system parameter estimation.
Assessment
40% assignments (2), 20% intermediate exam and 40% final exam, however
these percentages are indicative and may be varied at the
lecturer's discretion.
Details of the actual assessment used in a given year
can be found in the study guide provided at the start of the semester.
Resources
All the materials necessary for the course will be availabe on-line. The
lecture notes also include a bibliography for further reading on
the subject.