Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH212
Module Title: Ordinary Differential Equations and Control
Module Level: Level 2
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims Solving systems of linear autonomous differential equations. Based on this material an accessible introduction to the ideas of mathematical control theory is given. The emphasis here will be on the stability and stabilization of feedback. Phase plane techniques will be introduced.
 Learning outcomes A. Make use of the basic ideas in the theory of linear autonomous differential equations.B. Employ Laplace transform and matrix methods to the solution of differential equations.C. Recognise and work with elementary concepts from control theory, such as stability, stabilization by feedback and controllability.D. Solve simple control problems.E. Carry out simple phase plane analysis.
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus (a) Systems of linear ODEs: Normal form; solution of homogeneous systems; fundamental matrices and matrix exponentials; repeated eigenvalues; complex eigenvalues; stability; solution of non-homogeneous systems by variation of parameters. (b) Laplace transforms: Definition; statement of conditions for existence; properties including transforms of the first and higher derivatives, damping, delay; inversion by partial fractions; solution of ODEs; convolution theorem; solution of integral equations. (c) Linear control systems: Systems: state-space; impulse response and delta functions; transfer function; frequency response. (d) Stability: exponential stability; input-output stability; Routh-Hurwitz criterion. (e) Feedback: state and output feedback; servomechanisms. (f) Introduction to controllability and observability: definitions, rank conditions (without full proof) and examples. (g) Nonlinear ODEs: Phase plane techniques, stability of equilibria.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Formal Exam 80.00 2 Class Test 1 10.00 3 Class Test 2 10.00
 Module Catalogue generated from SITS CUT-OFF: 6/4/2020 6:42:58 AM