Introduction to discrete-time systems and signals. Representation of
discrete-time systems in time domain. Frequency domain representation
(Z-Transform). Basic theorems and formulae related to
Z-Transforms, Inverse Z-Transform ; Direct division,
Computational Method, Partial Fraction Expansion, Inverse Integral.
Relationship between Laplace domain and Z-domain; Forward and backward
difference, exponent relation, bilinear transformation, frequency
prewarping.
System Specifications- System stability; pole location,
Jury's Stability Criterion, Lienard-Chipart test. Static error
constants, time-domain
specifications, frequency domain specifications (Bode plots). Controller
design - Pole placement, Loop shaping; Nyquist
Criterion.
Discrete-time State Space representation. Structure and relationship
with continuous-time counterpart. Concepts : Controllability and
stabilizability , observability and detectibility. Non-asymptotic
behaviour. Controller design using state space. Discrete-time
observers (deterministic).
Observers, Functional Observers, Multirate Sampling, Multirate
Output Feedback, Multirate Sampling based Functional Observation
If possible :
Non-linear discrete-time systems - system analysis ,periodic
behaviour, chaos and
sarkovskii's theorem. Closed loop stability - Popov's stability
criterion. Controller design (specific cases) - feedback
linearisation.