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L2 - Gain and Passivity Techniques in Nonlinear Control
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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.
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