L2-Gain and Passivity Techniques in Nonlinear Control

Arjan Van Der Schaft

• 01 november 1999
• 9781852330736

Samenvatting:

This text discusses fundamental theories of nonlinear control. It details the small-gain and passivity theorems, and recent developments in nonlinear passivity-based and robust H-infinity control. This edition also includes new material on feedback passifiability.



This book gives a unified treatment of classical input-output stability theory and recent developments in nonlinear robust and passivity-based control. The synthesis between these areas is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this vantage-ground. The connection between L2-gain and passivity via scattering is detailed.The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasizing the close relations with modeling and control by interconnection. Feedback equivalence to a passive system and resulting stabilization strategies are discussed.The potential of L2-gain techniques in nonlinear control is demonstrated, including a compact treatment of the nonlinear H optimal control problem. This book supplies the reader with a succinct, informative summary of a fundamental and rapidly developing area of nonlinear control theory.