This unit aims to introduce linear system theory including state space representation, the structural properties of linear systems and the synthesis of linear controllers.


Teaching periods
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date

Learning outcomes

Students who successfully complete this unit will be able to:

  • Develop mathematical state space representations of continuous and discrete linear system (K1, K2, K3, S1)
  • Evaluate the state transition matrix, for linear and time varying systems (K1, K2, K3, S1)
  • Analyse and evaluate the structural properties of linear systems including controllability, observability and stability (K1, K2, K3, S1, S2)
  • Design and synthesize linear controllers using state feedback (K1, K2, K3, K4, S1, S2, S3)
  • Design asymptotic observers and compensators (K1, K2, K3, K4, S1, S2, S3)
  • Design optimum observers and controllers (K1, K2, K3, K4, S1, S2, S3)

Teaching methods


Type Hours per week Number of weeks Total (number of hours)
Face to Face Contact (Phasing out)
3.00 12 weeks 36
Face to Face Contact (Phasing out)
0.50 12 weeks 6
Face to Face Contact (Phasing out)
Science Laboratory
0.50 12 weeks 6
Unspecified Learning Activities (Phasing out)
Independent Learning
8.50 12 weeks 102


Type Task Weighting ULO's
ExaminationIndividual 60% 1,2,3,4,5,6 
Laboratory ReportIndividual 40% 1,2,3,4,5,6 


As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:

(i) an overall mark for the unit of 50% or more, and(ii) at least 40% in the final exam, and(iii) at least 40% of the possible marks for the laboratory hurdle.Students who do not successfully achieve hurdle requirements (ii) and (iii) will receive a maximum of 45% as the total mark for the unit.


  • Model classification, State Space models. Realization, controllable canonical forms
  • Observable canonical forms, Other realizations, minimal realization Linearization Solution to continuous-time LTI systems
  • Controllability
  • Observability, LTI system, duality
  • Controllability & observability for DT LTI systems
  • Kalman decomposition
  • State feedback, direct method
  • State feedback, canonical form method
  • State feedback, Lyapunov equation method, Stabilizability
  • Observer, detectability ,Observer-based control
  • Asymptotic Observers, Reduce order Observer
  • Continuous-time finite horizon LQR , Continuous-time infinite horizon LQR, Discrete-time LQR

Study resources

Reading materials

A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.