Aims

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.

Objectives

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.

Content

PART 1: MULTIVARIABLE FEEDBACK SYSTEMS (7L + 1 example class, Dr F Forni)

• Performance measures for multi-input/multi-output systems.
• Stabilization: stability conditions, all stabilizing controllers, small gain theorem.
• Models for uncertain systems.
• Robust stability and performance. Loop shaping design.
• Design of multivariable systems.

PART 2: NONLINEAR SYSTEMS (7L + 1 example class, Dr I Lestas)

• Linear and Nonlinear systems; feedback circuits.
• Differential equations and trajectories.
• Multiple equilibria, limit cycles, chaos and other phenomena.
• Examples from biology and mechanics.
• State space stability analysis:
• The theorems of Lyapunov, LaSalle invariance principle.
• Stability of nonlinear circuits and neural behaviors.
• State-space tools for robustness analysis.
• Input/output stability analysis:
• Describing functions
• Small gain theorems, circle and Popov criteria, passivity.