Undergraduate Teaching

Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2021-22

Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2021-22

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Module Leader

Prof R Sepulchre


Prof R Sepulchre and Dr F Forni

Timing and Structure

Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework


3F2 assumed.


The aims of the course are to:

  • introduce fundamental concepts from nonlinear dynamic systems
  • introduce techniques for the analysis and control of nonlinear and multivariable systems.


As specific objectives, by the end of the course students should be able to:

  • apply standard analysis and design tools to multivariable and nonlinear feedback systems.
  • appreciate the diversity of phenomena in nonlinear systems.


Part I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof R. Sepulchre)

1. Uncertainty and Nonlinearity in control systems: simple models.

2. Signal spaces and system gains.

3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties

4. Dissipativity theory

5. Robust stability and performance. Stability margins.

6. An introduction to H-infty control. 

7. Gap metrics

PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Dr F Forni)

1. Small and large signal analysis. Contractive systems. Fading memory operators.

2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.

3. Feedback systems: simple models.

4. Phase portrait analysis.

5. Analysis and design of switches and clocks. Robust differential control.

6. Monotone systems. Contraction of cones. Polyhedral cones. Applications in biology.

7. Describing function analysis.

Further notes


Coursework only.


Coursework Format

Due date

& marks

[Coursework activity #1  Robust control of haptic interfaces

Coursework 1 brief description

Learning objective:

  • Learn how to model uncertainty in an engineering application
  • Design a robust controller in Matlab

Individual Report 

  anonymously marked


25 February 2022


[Coursework activity #2  Feedback oscillations control ]

Coursework 2 brief description

Learning objective:

  • Learn how to model and analyse nonlinear oscillations in feedback systems
  • Design a nonlinear oscillator in a biologically motivated appication

Individual Report

anonymously marked

  25 March 2022




Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.


The UK Standard for Professional Engineering Competence (UK-SPEC) describes the requirements that have to be met in order to become a Chartered Engineer, and gives examples of ways of doing this.

UK-SPEC is published by the Engineering Council on behalf of the UK engineering profession. The standard has been developed, and is regularly updated, by panels representing professional engineering institutions, employers and engineering educators. Of particular relevance here is the 'Accreditation of Higher Education Programmes' (AHEP) document which sets out the standard for degree accreditation.

The Output Standards Matrices indicate where each of the Output Criteria as specified in the AHEP 3rd edition document is addressed within the Engineering and Manufacturing Engineering Triposes.

Last modified: 27/09/2021 09:29