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L2-Gain and Passivity Techniques in Nonlinear Control

By (author) Arjan van der Schaft

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This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems.Â Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection betweenÂ L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed.Â The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leadingÂ to novel control methodologies going beyond passivity. The potential ofÂ L2-gain techniquesin nonlinearÂ control,Â including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with aÂ geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization. Â Â·Â Â Â Â Â Â Â Â Â L2-Gain and Passivity Techniques in NonlinearÂ Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: Â·Â Â Â Â Â Â Â Â Â updatedÂ and extended coverage of dissipative systems theory Â·Â Â Â Â Â Â Â Â Â substantial new material regarding converse passivity theorems and incremental/shifted passivity Â·Â Â Â Â Â Â Â Â Â coverageÂ of recent developments on networks of passive systems with examples Â·Â Â Â Â Â Â Â Â Â a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics Â·Â Â Â Â Â Â Â Â Â updated treatment of all-pass factorization of nonlinear systems Â The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.

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