Semester Offering: InterSem
First part of this course covers analytical tool for studying a nonlinear system; such as, phase plane analysis, Lyapunov function and describing function. Second part of this course covers major nonlinear controller design techniques; such as, feedback linearization, sliding control and adaptive control.


    I. Phase Plane Analysis
    1. Concepts of Phase Plane
    2. Constructing Phase Portraits
    3. Existence of Limit Cycles
    4. Multiple (Isolated) Equilibria and Bifurcation

    II. Lyapunov Theory
    1. Concepts of Stability
    2. Linearization and Local Stability
    3. Lyapunov's Direct Method
    4. System Analysis and Control Design Based on Lyapunov's Direct Method

    III. Describing Function Analysis
    1. Fundamental - Definition and Computing Describing Function
    2. Common Nonlinearities in Control System
    3. Describing Function of Common Nonlinearities
    4. Describing Function Analysis of Nonlinear Systems

    IV Feedback Linearization
    1. Mathematical Tool - Lie Derivatives and Brackets
    2. Input-State Linearization
    3. Input-Output Linearization
    4. Zero Dynamics and Normal Form

    V Sliding Control
    1. Sliding Surfaces - Filippov's Construction of the Equivalent Dynamics
    2. Continuous Approximations of Switching Control Laws
    3. Performance Trade-Off

    VI Adaptive Control
    1. Concepts of Adaptive Control
    2. Adaptive Control of Linear Systems with Full State or Output Feedback
    3. Adaptive Control of Nonlinear Systems
    4. On-Line Parameter Estimation
    5. Composite Adaptation

    VII Physical Applications for Nonlinear Control
    1. Robotics - Position and Trajectory Control
    2. Adaptive Robot Trajectory Control


  1. Modern Control Theory. W.L. Brogan (2nd Ed), Prentice-Hall, 1985
  2. Applied Nonlinear Control. J.J. Slotine and W. Li., Prentice-Hall, 1991
  3. Nonlinear Systems, H.K. Khalil, (3rd Edition), Prentice-Hall, 2001
  4. Nonlinear Control Systems, A. Isidori (3rd Edition), Springer, 1995