L2-Gain and Passivity Techniques in Nonlinear Control

1. Front Matter

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2. Input-output stability

   Pages 7-15

3. Small-gain and passivity

   Pages 16-31

4. Dissipative systems theory

   Pages 32-52

5. Hamiltonian systems as passive systems, and stabilization of Hamiltonian systems

   Pages 53-68

6. Factorizations of nonlinear systems

   Pages 69-90

7. Nonlinear H _∞ control

   Pages 91-119

8. Hamilton-Jacobi inequalities

   Pages 120-154

9. Back Matter

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The aim of these lecture notes is to provide a synthesis between classical input-output and closed-loop stability theory, in particular the small-gain and passivity theorems, and recent work on nonlinear H( and passivity-based control. The treatment of the theory of dissipative systems is the main aspect of these lecture notes. Fundamentals of passivity techniques are summarised, and it is shown that the passivity properties of different classes of physical systems can be unified within a generalised Hamiltonian framework. Key developments in linear robust control theory are extended to the nonlinear context using L2-gain techniques. An extensive treatment of nonlinear H( control theory is presented, emphasising its main structural features. Since the application of L2-gain techniques relies on solving Hamilton-Jacobi inequalities the structure of their solution sets and conditions for solvability are derived.

• control
• control theory
• nonlinear control
• robust control
• stability
• stability theory

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